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  <h2>FE000000 Guide</h2>
  <h3><span id="e0"></span></h3>
  <p>This guide divides the game into part based (more or less) on which of the <span id="e1"></span> goals in the "Goals" tab have been accomplished so far.</p>
  <p>Note that this guide was mostly written based on a playthrough which was very active and did not use offline progress. The times given are thus fairly close to minimum possible times. However, this playthrough was done before achievements were added, so the achievement bonus makes it possible to go slightly faster.</p>
  <p>Show all guide parts: <input id="b0" type="checkbox"></input></p>
  <div style="width: 1024px; margin-left: auto; margin-right: auto;">
    <button id="b1" onclick="Tabs.setTab(1)">Before sacrifice</button>
    <button id="b2" onclick="Tabs.setTab(2)">Sacrifice to prestige</button>
    <button id="b3" onclick="Tabs.setTab(3)">Prestige to infinity</button>
    <button id="b4" onclick="Tabs.setTab(4)">Infinity to breaking infinity</button>
    <button id="b5" onclick="Tabs.setTab(5)">Breaking infinity to starting Infinity Challenge 1</button>
    <button id="b6" onclick="Tabs.setTab(6)">Starting Infinity Challenge 1 to eternity</button>
    <button id="b7" onclick="Tabs.setTab(7)">Eternity to completing all eternity milestones</button>
    <button id="b8" onclick="Tabs.setTab(8)">Completing all eternity milestones to unlocking the Eternity Producer</button>
    <button id="b9" onclick="Tabs.setTab(9)">Unlocking the Eternity Producer to starting Eternity Challenge 1</button>
    <button id="b10" onclick="Tabs.setTab(10)">Starting Eternity Challenge 1 to unlocking chroma</button>
    <button id="b11" onclick="Tabs.setTab(11)">Unlocking chroma to complexity</button>
    <button id="b12" onclick="Tabs.setTab(12)">Complexity to completing all complexity achievements</button>
    <button id="b13" onclick="Tabs.setTab(13)">Completing all complexity achievements to unlocking powers</button>
    <button id="b14" onclick="Tabs.setTab(14)">Unlocking powers to unlocking galaxies</button>
    <button id="b15" onclick="Tabs.setTab(15)">Unlocking galaxies to finality</button>
    <button id="b16" onclick="Tabs.setTab(16)">After finality</button>
  </div>
  <div id="b17">
    <h3>Before sacrifice</h3>
    <p>This part of the game is fairly simple. Start by clicking the "Main" button to go to the main tab, if you haven't already. Then buy a Generator 1 for the cost of <span id="e2"></span> stars. Other generators will become affordable over time. You can hold down M to buy max of all generators. The way generators work is very simple. Each generator produces the one before it, except the first which produces stars. Buying more of a generator increases a multiplier to its production, by <span id="e3"></span>^(<span id="e4"></span> / <span id="e5"></span>), which is <span id="e6"></span>x, per purchase.</p>
    <p>Generator initial costs: <span id="e7"></span>^(generator number^<span id="e8"></span>) stars</p>
    <p>Generator cost increases per purchase: (<span id="e9"></span>^generator number)x stars</p>
    <p>It doesn't matter very much in what order you buy generators, but generally buying a generator you don't have any of is best, and otherwise cheaper and lower generators are better than higher ones. Buying max will generally automatically buy generators in this order (first buying generators you don't have any of, then repeatedly buying the cheapest generator possible).</p>
    <p>The autobuyer tab is also useful at this point. You can buy "slow" autobuyers for stars, and they will each automatically buy a certain generator every <span id="e10"></span> (which is why they are called "slow"). They are automatically set to buy max, and you should probably keep them there because then, if they can buy more than <span id="e11"></span> of a generator when they trigger, they will do so (if set to buy singles they will only buy <span id="e12"></span>). You should generally buy an autobuyer as soon as you have bought all generators with the same price or a lower price.</p>
    <p>Once you get <span id="e13"></span> stars, several things will happen more or less at once. Firstly, you can buy the last generator, your first Generator 8. There is no Generator 9, so this is somewhat significant. Secondly, you can buy a boost. This will multiply all your generator multipliers by <span id="e14"></span> when bought. Thirdly, after buying Generator 8, you will be able to sacrifice. It doesn't matter very much for what multiplier you do this the first time, but I would recommend at least <span id="e15"></span>x, and getting the boost with cost <span id="e16"></span> stars.</p>
    <p>When you sacrifice, you'll be asked if you're sure you want to. You should say yes. This is a measure to stop accidental sacrifices at bad times for it. Turn it off in the options tab (in the confirmations row) when you feel that the safety of not accidentally sacrificing stops being worthwhile. This applies to other confirmations too.</p>
  </div>
  <div id="b18">
    <h3>Sacrifice to prestige</h3>
    <p>So, you've sacrificed. This resets all Generator 1-7 amounts, but they keep their multipliers, and Generator 8 actually has a slightly increased (<span id="e17"></span>x) multiplier. Thus, it should only take roughly <span id="e18"></span> for you to get back to the same star production you had before. After this, keep playing as before. There'll be another boost at <span id="e19"></span> stars. Note that in general boosts are the most worthwhile things to buy, since they give a multiplier to all generators.</p>
    <p>Sacrifice formula: (log<span id="e20"></span>(stars when sacrificing) / <span id="e21"></span>) sacrifice multiplier</p>
    <p>At <span id="e22"></span> stars, you will be able to prestige. The slow Generator 8 autobuyer also costs <span id="e23"></span> stars, so unless you're very active you probably want to buy that autobuyer first. However, after buying that, prestige as soon as you can.</p>
  </div>
  <div id="b19">
    <h3>Prestige to infinity</h3>
    <p>So, you've prestiged. This resets all Generator 1-8 amounts and multipliers, and your stars. However, you now have a roughly <span id="e24"></span>x multiplier to all generators, which will let you get far more quickly to where you were before. You also keep your slow autobuyers. Keep playing as before, perhaps sacrificing slightly later, at perhaps <span id="e25"></span>x (though it barely matters). Eventually you'll be able to prestige again. In theory, the optimal prestige powers amounts to prestige at are roughly <span id="e26"></span>, <span id="e27"></span>, <span id="e28"></span>, <span id="e29"></span>, and <span id="e30"></span>, but you may want to prestige slightly less often so that you have to buy generators and boosts less, especially if you are idle. Consistently prestiging for <span id="e31"></span>x or <span id="e32"></span>x is not that bad.<p>
    <p>If you are idle, it might be worth pushing on your second prestige to <span id="e33"></span> stars to unlock the slow boost autobuyer, the last slow autobuyer. This will give you roughly <span id="e34"></span> prestige power, or a <span id="e35"></span>x prestige multiplier if you first prestiged for <span id="e36"></span> prestige power.</p>
    <p>Prestige formula: (stars when sacrificing^<span id="e37"></span> / <span id="e38"></span>) prestige power</p>
    <p>Note that prestige power gain (and sacrifice multiplier gain, for that matter) is based on highest stars since last prestige (or since last sacrifice), so buying something right before prestiging or sacrificing won't decrease the gained multiplier, but will stop that gained multiplier from going up for some time as stars increase to their previous maximum value.</p>
    <p>Keep prestiging as described above (for the above amounts, or <span id="e39"></span>x or <span id="e40"></span>x). Sacrifice once in each prestige, <span id="e41"></span> to <span id="e42"></span> after prestiging (or when progress feels like it's starting to slow). If you're close to <span id="e43"></span> stars (if you have more than <span id="e44"></span>, perhaps) it's probably best not to prestige, because stuff happens at <span id="e45"></span> stars. Specifically, stars will stop increasing. Also, the main tab will vanish, and be replaced with a message saying "The universe has collapsed due to an excess of stars." (I guess that's why stars stopped increasing.) Also, a new button will appear, saying "Infinity: Gain 2 infinity points", with additional statistics on it. Press this button, and infinity, as soon as it appears; unlike with sacrifice and prestige, there's nothing to be gained from waiting at this point.</p>
  </div>
  <div id="b20">
    <h3>Infinity to breaking infinity</h3>
    <p>So, you've infinitied. This resets everything prestige resets, and also resets prestige power. However, you keep your slow autobuyers. New tabs called "Infinity" and "Normal Challenges" also unlock. On the Infinity tab, you can see that you have <span id="e46"></span> infinity points and <span id="e47"></span> infinity (infinities are basically a count of how many times you've infinitied). Buy an Infinity Generator 1 for the <span id="e48"></span> infinity points you just got. Note that infinity generators (IGs) have the same initial costs, cost increases, and multiplier per purchase as the generators you already know from pre-infinity (for clarity, in this guide the pre-infinity generators are sometimes called normal generators, though sometimes they are called generators when it is (hopefully) clear); they just cost IP instead of stars. Infinity will reset infinity stars to <span id="e49"></span> infinity generator amounts to however many you've bought, but will not reset their multipliers.</p>
    <p>There will be something on the autobuyer tab that appears to let you turn the infinity autobuyer on (checked) or off (unchecked). It indeed does, but since the infinity autobuyer is locked it doesn't do anything whether it's on or off yet. It doesn't really matter whether you turn it on or off right now; by the time you unlock it you'll be changing its other settings a lot too. In general, if an autobuyer does something that resets things in the way that (as you just saw) infinity does, it will be possible to turn it off before unlocking it, so it doesn't reset things right after it's unlocked and before it can be turned off. This is also why the above "Turn newly unlocked autobuyers on when unlocked" setting exists.</p>
    <p>You can do Normal Challenge 1 right now. If you want to do so, you should read below about normal challenges and Normal Challenge 1 in particular. Do another infinity, whether or not you do it in Normal Challenge 1, generally following the parts of the guide above this (except that you don't need to unlock slow autobuyers, since they're already unlocked). It'll be a lot quicker (probably at least <span id="e50"></span>x quicker), since you'll have a <span id="e51"></span>x multiplier to normal generators from having produced <span id="e52"></span> infinity points (the formula for this multiplier is (<span id="e53"></span> + total infinity points / <span id="e54"></span>), capped at <span id="e55"></span>), and there'll be an increasing multiplier to normal generators from infinity stars, produced by your Infinity Generator 1. Due to this infinity being quicker, you don't need to wait as long to sacrifice; generally you should sacrifice once each prestige, when the number of stars you need to prestige is roughly <span id="e56"></span>x your current stars.</p>
    <p>After you infinity for the second time, you'll have <span id="e57"></span> unspent infinity points, which you can't buy anything with. Do the same thing again but slightly quicker. Now the multiplier from total IP is <span id="e58"></span>x and since you have <span id="e59"></span> infinities rather than <span id="e60"></span>, infinity stars will be produced <span id="e61"></span>x faster (infinity generators are all multiplied by min(<span id="e62"></span>, infinities / <span id="e63"></span>), meaning that more infinities make them stronger up to <span id="e64"></span>), giving roughly a <span id="e65"></span>x additional multiplier to generators. After you infinity for the third time, you'll have <span id="e66"></span> IP and be able to buy Infinity Generator 1 again. Now you're ready to start doing normal challenges.</p>
    <p>Normal challenges are much like normal infinities, but they have special conditions to make them harder and give you an autobuyer (or make one of your autobuyers trigger every tick) on completion. Also, all generators are multiplied by <span id="e67"></span>^(completed normal challenges / <span id="e68"></span>). To do a normal challenge, go to the Normal Challenges tab and click its "Start challenge" button. In theory any of the normal challenges could be done immediately, but some are much easier than others. Also, some challenges (1, 2, and 12) start out similar to a normal infinity and don't get easier as you progress by as much as the other normal challenges. These are marked with "Consistent" because they take a more consistent amount of time with progress than the others. I found 1 easy and 2 and 12 hard, but other people have different views which may be more correct.</p>
    <p>Below is information on each normal challenge (including strategy), followed by a description of general strategy.</p>
    <p>Normal Challenge 1: Consistent. If you could somehow do it as your first infinity, it would be faster than a normal first infinity. As a second infinity, it's slightly slower than a normal infinity, but not by much. Later, it gets noticeably slower compared to a normal infinity. After you have <span id="e69"></span> of each generator the only generators worth buying are Generator 1 and (to a small extent) Generator 8. If you're fairly active, you might want to turn some of your autobuyers off and buy Generators 1 and 8 manually due to this. (Boosts are still worth buying though.) Also, don't sacrifice in this challenge because it's useless.</p>
    <p>Normal Challenge 2: Consistent. This challenge is somewhat slow, and doesn't speed up as much with progress as normal infinities and most challenges do. The important thing for this challenge is not to be buying things constantly (so you can't always be buying max), because buying almost anything resets the generator multipliers and they take a while to recover. At this point, buying things roughly every <span id="e70"></span> is good. You can do Normal Challenge 2 very early if you want (buying things less frequently, maybe even only once per minute). You can buy things on some interval by setting autobuyers to trigger every <span id="e71"></span> (in which case you probably want to synchronize your slow and fast autobuyers), or do it manually.</p>
    <p>Normal Challenge 3: Easy. The only hard part of this is the very start, when you don't have any generators higher than Generator 1. However, due to the very small multiplier on Generator 1 (starting at <span id="e72"></span>), this will be the case for a few minutes at the start, which you just have to mostly wait for. Buying Generator 1 a second time for <span id="e73"></span> stars will let you get Generator 2 sooner, but buying it a third time for <span id="e74"></span> stars won't, so buy it twice and not a third time. Once you get <span id="e75"></span> stars and buy Generator 2 it should be fairly hard to even notice you're in a challenge. After you first prestige in Normal Challenge 3, there'll be a short wait until you can get Generator 2 again, but this time it should be less than a minute. It's worth noting that overnight, you can do Normal Challenge 3 at any point, since its increasing multiplier to Generator 1 will have the same effect as an additional <span id="e76"></span>x multiplier to all generators for every <span id="e77"></span> (a bit more than <span id="e78"></span>) you wait. After <span id="e79"></span> or so this is enough to easily get you to infinity.</p>
    <p>Normal Challenge 4: Easy. This challenge doesn't have much special strategy, but you might want to wait to make a purchase of a higher generator (any generator other than Generator 1, but especially the highest few) until you can buy many at once (more explicitly, get roughly <span id="e80"></span> times more stars than last time you bought things), since when you buy a higher generator you'll have to wait for all the ones below it to reach their previous levels again before you reach your prior star production.</p>
    <p>Normal Challenge 5: Medium. This challenge starts out reasonable but gets harder due to you "missing" more purchases. It doesn't have any special strategy.</p>
    <p>Normal Challenge 6: Hard. This challenge might seem not that bad at first, but it gets a lot harder later due to you missing <span id="e81"></span> generator multipliers. It doesn't have any special strategy, though note that you can't sacrifice due to not getting Generator 8.</p>
    <p>Normal Challenge 7: Hard. This challenge doesn't take too long (it's only a bit harder than Normal Challenge 5 if you do it right) but it requires autobuyers to be off and has some strategy. Don't feel worried about doing prestiges; you can do prestiges even for <span id="e82"></span>x and you'll have a lot of purchases left over if you follow the advice here. For all prestiges but your last, buy only <span id="e83"></span> of each generator (you can buy as many boosts as you want). For your last prestige (this is best to do when you have over <span id="e84"></span> stars), turn the prestige autobuyer off (or otherwise make sure you don't prestige), buy as many Generator 8 as you can, then buy as many Generator 1 as you can. If you have leftover purchases, buy as many Generator 2 as you can. You should then wait until you can infinity.</p>
    <p>Normal Challenge 8: Medium. This challenge is actually a bit faster than a normal infinity for most of the first prestige, but then gets slower at the end. It doesn't have any special strategy.</p>
    <p>Normal Challenge 9: Medium. This challenge is on the easy side of medium, and, like the other medium challenges, gets harder at the end. It doesn't have any special strategy.</p>
    <p>Normal Challenge 10: Hard. This challenge is almost like a different game. Buy <span id="e85"></span> of each generator (it's all you can buy), then sacrifice. Repeat (it'll probably take <span id="e86"></span> repetitions or so before you can infinity and finish the challenge, though it gets quicker with more infinity stars). Once you can sacrifice each time, only wait a few seconds to do so; waiting longer is basically a waste of time (and not waiting at all is fine).</p>
    <p>Normal Challenge 11: Medium. As you'd probably expect, this challenge gets harder at the end. It doesn't have any special strategy.</p>
    <p>Normal Challenge 12: Consistent. This is like pre-infinity, but faster and with better automation. It doesn't have any special strategy; just do what you did first infinity. It might seem like this would be a good early challenge. However, actually infinity stars speed up a normal infinity quite a lot compared to Normal Challenge 12, and so you can do several normal infinities in the time it'd take you to do Normal Challenge 12. Furthermore, Normal Challenge 12 is sped up somewhat by the multiplier to normal generators based on total infinity points. Thus, Normal Challenge 12 is best to do either last or because you want to be able to do infinities automatically.</p>
    <p>In this paragraph, challenge orders within each sentence are suggestions and not following them probably won't make anything much harder. Do Normal Challenge 1 (if you didn't do it already as your second infinity), Normal Challenge 3, and Normal Challenge 4 in <span id="e87"></span> separate infinities. Then do <span id="e88"></span> normal infinities (each of which is roughly <span id="e89"></span> long if you are active). Spend your <span id="e90"></span> IP on an Infinity Generator 2. Then do Normal Challenges 5, 8, 9, and 11. Spend <span id="e91"></span> IP on the first infinity upgrade, increasing the multiplier per boost from <span id="e92"></span>x to <span id="e93"></span>x. Optionally do some more normal infinities now if you want. Do Normal Challenges 2, 6, 7, 10, and 12, and then, having completed all normal challenges, break infinity in the Infinity tab.</p>
    <p>For autobuyers, you probably want to sacrifice for multiplier <span id="e94"></span>x, prestige for multiplier <span id="e95"></span>x, and, if you do Normal Challenge 12 earlier than suggested here, infinity whenever possible, at least before breaking infinity (multiple settings lead to this).</p>
  </div>
  <div id="b21">
    <h3>Breaking infinity to starting Infinity Challenge 1</h3>
    <p>So, you've broken infinity. You can now get more infinity points from each infinity, if you get more stars. At the very start, you want to do slightly long infinities just to find out how many IP to infinity for so that you get the most IP/sec (infinity points per second), then do shorter infinities in each of which you get that many IP. (Of course, with this guide, finding out yourself how many IP to infinity for is mostly unnecessary.) Once IP/sec starts going down, it generally won't go back up in that infinity, except sometimes if you are about to be able to buy another boost (so that might be worth checking).</p>
    <p>Note that you cannot go beyond <span id="e96"></span> stars in normal challenges even if infinity is broken, so don't try to, for example, spend months in Normal Challenge 3 to get exponential infinity point gain. Also note that although you can now view the Infinity Challenges tab, it is not useful for a while.</p>
    <p>IP formula: stars^<span id="e97"></span></p>
    <p>The order to buy things in is, most importantly, new infinity generators, second-most importantly, infinity upgrades (with the second being better than the first when they have the same cost), and least importantly, infinity generators you already have (these are so unimportant that even if they cost <span id="e98"></span>x the price of a new infinity generator or an infinity upgrade, you shouldn't buy them).</p>
    <p>Here are some example infinity point gain statistics (yours might be different due to having a different number of total IP or infinities). First get <span id="e99"></span> IP per infinity with IP/sec going from roughly <span id="e100"></span> (right after breaking infinity) to roughly <span id="e101"></span>. After buying the first infinity upgrade for <span id="e102"></span> IP (increasing the per-boost multiplier to <span id="e103"></span>, which is a lot more useful than the first time now that you can get more boosts), get <span id="e104"></span> IP per infinity with IP/sec going from roughly <span id="e105"></span> to roughly <span id="e106"></span>.</p>
    <p>After buying Infinity Generator 3 (which, to repeat, you should do before buying the first infinity upgrade for <span id="e107"></span> IP), you'll notice that IP/sec stops really going down at all (it might occasionally go down a little, but when you get your next boost it will mostly go back up). Do a single infinity for roughly <span id="e108"></span>, getting <span id="e109"></span> IP. Buy the first infinity upgrade again. Now (you can do this slightly later or earlier) start doing infinities for <span id="e110"></span> IP until you have <span id="e111"></span> infinities (to increase infinity generator multipliers). This should take roughly <span id="e112"></span> per infinity at first, decreasing to <span id="e113"></span>. After that, again do a single long infinity, this time for roughly <span id="e114"></span> and for <span id="e115"></span> IP. The first two infinity upgrades should both have that cost; they're roughly equally good but the second is slightly better, so buy it. Now do another infinity for roughly <span id="e116"></span>, but still for <span id="e117"></span> IP, and buy the first infinity upgrade.</p>
    <p>At this point you're on your own, because a long list of exact infinities seems like too much detail. Generally try to make sure that after every infinity, with the IP you got, you unlock an infinity upgrade, unlock a new infinity generator, or can make a lot (e.g., <span id="e118"></span>) infinity generator purchases. On the other hand, if you're getting more than <span id="e119"></span>x total IP per infinity at this point, your infinities are probably too long. You may want to get a bit more IP than the price of whatever you want to purchase, so that you can also buy some cheap infinity generators. Infinities will get longer at first, getting as long as <span id="e120"></span> to <span id="e121"></span> (how long your longest infinity is depends on how much more IP you try to infinity for each time), but past <span id="e122"></span> IP infinities will get a bit shorter again, more specifically, <span id="e123"></span> to <span id="e124"></span> long. The infinity autobuyer isn't that useful in this part, but if you know how much IP you want to infinity for, then you can set it to that.</p>
    <p>At <span id="e125"></span> stars, which you can reach in roughly <span id="e126"></span> from <span id="e127"></span> IP, Infinity Challenge 1 should become unlocked and thus possible to start. Don't start it until you get the first infinity upgrade costing <span id="e128"></span> IP and the second infinity upgrade costing <span id="e129"></span> IP. Note that after buying the second infinity upgrade for <span id="e130"></span> IP, it will be maxed and you will not be able to buy it again its effect should now be that generators are multiplied by (infinity stars)^<span id="e131"></span>, rather than the original (infinity stars)^<span id="e132"></span>. Anyway, you can now start Infinity Challenge 1, so do that. The next section of the guide becomes visible when you complete Infinity Challenge 1, so information on how to do so is in this section (it is also repeated in the next section).</p>
    <p>Infinity challenges (or ICs) are much like normal challenges, except they require more stars to infinity than a normal infinity (you cannot go beyond their star requirement in them whether or not infinity is broken), and after completing them you get some new bonus to something rather than getting an autobuyer and get a multiplier to infinity generators of <span id="e133"></span>^(completed infinity challenges / <span id="e134"></span>) rather than a multiplier to normal generators. Infinity challenges can generally be grouped into the easy ones with no special strategy and the hard ones with special strategy. Unlike the previous normal challenges, they unlock in a particular order, which is also the order you should complete them in.</p>
    <p>Infinity Challenge 1: Hard. This is a bunch of normal challenges combined (Normal Challenges 2, 3, 4, 5, 6, and 7), and its strategy is mostly taken from Normal Challenge 7, so follow the strategy given above for that challenge. The differences are that you want to spend at least <span id="e135"></span> before prestiging (to build up infinity stars and thus do fewer prestiges, letting you save more purchases for the last prestige), you want to spend at least <span id="e136"></span> in each prestige (again, to do fewer prestiges; time in current prestige can be viewed in the Statistics tab, but estimating it should also work), your last prestige should instead be when you reach over <span id="e137"></span> stars (because of the goal of <span id="e138"></span> being far higher than the goal for Normal Challenge 7), and that at the end you should buy Generator 6 rather than Generator 8, because Generator 8 does not exist due to Normal Challenge 6. Despite Normal Challenge 2 making boosts reset multipliers, boosts are worth buying as soon as you can afford them. You don't have to worry about sacrifice because, due to Normal Challenge 6, you can't do it. Infinity Challenge 1 should take <span id="e139"></span> to <span id="e140"></span>. It's perhaps worth noting that you can complete this challenge eventually just by buying a Generator 1 and waiting, since it includes Normal Challenge 3, but this will take a day at least.</p>
  </div>
  <div id="b22">
    <h3>Starting Infinity Challenge 1 to eternity</h3>
    <p>Infinity challenges (or ICs) are much like normal challenges, except they require more stars to infinity than a normal infinity (you cannot go beyond their star requirement in them whether or not infinity is broken), and after completing them you get some new bonus to something rather than getting an autobuyer and get a multiplier to infinity generators of <span id="e141"></span>^(completed infinity challenges / <span id="e142"></span>) rather than a multiplier to normal generators. Infinity challenges can generally be grouped into the easy ones with no special strategy and the hard ones with special strategy. Unlike the previous normal challenges, they unlock in a particular order, which is also the order you should complete them in.</p>
    <p>Infinity Challenge 1: Hard. This is a bunch of normal challenges combined (Normal Challenges 2, 3, 4, 5, 6, and 7), and its strategy is mostly taken from Normal Challenge 7, so follow the strategy given above for that challenge. The differences are that you want to spend at least <span id="e143"></span> before prestiging (to build up infinity stars and thus do fewer prestiges, letting you save more purchases for the last prestige), you want to spend at least <span id="e144"></span> in each prestige (again, to do fewer prestiges; time in current prestige can be viewed in the Statistics tab, but estimating it should also work), your last prestige should instead be when you reach over <span id="e145"></span> stars (because of the goal of <span id="e146"></span> being far higher than the goal for Normal Challenge 7), and that at the end you should buy Generator 6 rather than Generator 8, because Generator 8 does not exist due to Normal Challenge 6. Despite Normal Challenge 2 making boosts reset multipliers, boosts are worth buying as soon as you can afford them. You don't have to worry about sacrifice because, due to Normal Challenge 6, you can't do it. Infinity Challenge 1 should take <span id="e147"></span> to <span id="e148"></span>. It's perhaps worth noting that you can complete this challenge eventually just by buying a Generator 1 and waiting, since it includes Normal Challenge 3, but this will take a day at least.</p>
    <p>The Infinity Challenge 1 reward uncaps the multiplier to normal generators based on total IP, which, at this point, gives normal generators at least an additional <span id="e149"></span>x multiplier. This means that your next few infinities will be very quick; for example, you can now get enough IP to buy Infinity Generator 6 for the first time (<span id="e150"></span> IP) in a infinity that is <span id="e151"></span> long (which is a reasonable thing to do strategically if you want). Infinities are now so short that they are a bit limited by autobuyers. In this part of the game, try to infinity for roughly <span id="e152"></span>x total IP each time (though it's OK to infinity earlier if that would let you get a new infinity generator that you don't have yet). You can do roughly this (definitely close enough) with the infinity autobuyer by setting its mode to "X times best of last ten" and its input to <span id="e153"></span>, though you'll still have to buy infinity upgrades (well, the one of them that isn't yet maxed) and infinity generators. Infinities will get slightly longer over time, going roughly from <span id="e154"></span> to <span id="e155"></span>, until you unlock Infinity Challenge 2. When you unlock Infinity Challenge 2, infinity and then start it.</p>
    <p>Infinity Challenge 2: Easy. Sacrifice formula is stars^<span id="e156"></span>, but since prestige is square-rooted there's a fairly big overall nerf. The challenge still doesn't require any special strategy, though. However, it does take roughly <span id="e157"></span>.</p>
    <p>The Infinity Challenge 2 reward increases the sacrifice formula to stars^<span id="e158"></span>, if it's bigger than the old formula (which it usually is). This is equivalent to almost a <span id="e159"></span>x multiplier to each normal generator. This will, as before, make your next few infinities far quicker. Also, due to your extra infinity generators making infinity stars increase faster and thus making longer infinities better, start to infinity for <span id="e160"></span>x IP rather than <span id="e161"></span>x. The length of infinities will increase from <span id="e162"></span> (right after IC2 completion) to <span id="e163"></span>, until you unlock Infinity Challenge 3. Infinity Challenge 3 is somewhat hard, so it might be worth getting somewhat more IP before starting it, even after you unlock it.</p>
    <p>Infinity Challenge 3: Hard. Be very careful about when you prestige; turn the prestige autobuyer off (though you can leave all others on). Prestige for at least <span id="e164"></span>, <span id="e165"></span>, <span id="e166"></span> and <span id="e167"></span> prestige power in your first <span id="e168"></span> prestiges, in that order; after that, you won't be able to prestige again. It can take up to <span id="e169"></span> (mostly spent in the first prestige), but it's shorter if you got more IP before starting it.</p>
    <p>Compared to previous IC rewards, the IC3 reward is rather weak. Infinities will still be roughly <span id="e170"></span> to <span id="e171"></span> long until you unlock IC4 (which should only take a few more infinities).</p>
    <p>Infinity Challenge 4: Hard. This infinity challenge is best done with your autobuyers set to trigger only every <span id="e172"></span>, and with your prestige autobuyer set in such a way that you gain a significant multiplier each time (setting its mode to time and its input to <span id="e173"></span> is good); it then takes roughly <span id="e174"></span>. You can slightly speed it up by manually prestiging somewhat earlier for the first few prestiges, or by manually buying things quicker at the start of each prestige, which makes it somewhat shorter.</p>
    <p>Since the IC4 reward is roughly linear with time in infinity (<span id="e175"></span> + seconds in infinity / <span id="e176"></span>), it rewards longer infinities. Thus, it is now best to infinity for <span id="e177"></span> times best of last ten rather than <span id="e178"></span> times. Infinities will still be <span id="e179"></span> to <span id="e180"></span> long (though remember that you're making roughly twice as much progress per infinity) until you unlock IC5.</p>
    <p>Infinity Challenge 5: Easy. This infinity challenge doesn't have any special strategy. The infinity challenge condition means in practice that every prestige starts with a few useless seconds, so you might think that setting your prestige autobuyer to <span id="e181"></span> or something like that is good because it will stop you from doing a lot of useless short prestiges, but in reality you can leave it at <span id="e182"></span>x and the challenge will take roughly as long as it would otherwise, because you still have to wait for infinity stars to build up. This is a rather fast infinity challenge, taking only roughly  <span id="e183"></span>.</p>
    <p>The IC5 reward is, initially, slightly worse than the IC3 reward, so it doesn't really change much. Continue to infinity for <span id="e184"></span>x. Infinities will still be <span id="e185"></span> to <span id="e186"></span> long until you unlock IC6, in <span id="e187"></span> or <span id="e188"></span> more infinities.</p>
    <p>Infinity Challenge 6: Hard. This infinity challenge requires you to turn your prestige autobuyer off. In this description of IC6 strategy, "prestige formula" refers to the formula for prestige power shown in the main tab (so initially ^<span id="e189"></span>, then ^<span id="e190"></span> after you first prestige, then ^<span id="e191"></span> again, and so on). In your first prestige, when the prestige formula is normal (^<span id="e192"></span>), get <span id="e193"></span> stars, then prestige. Having, for example, <span id="e194"></span> times more or less stars than <span id="e195"></span> when you prestige is not bad, but having <span id="e196"></span> times more or less stars is bad. Prestiging with fewer stars than recommended is bad because you'll have less prestige power than expected, and prestiging with more stars than recommended is bad because it will be hard to prestige again. Right now, prestiging with <span id="e197"></span> stars should be fairly easy because your production is slow enough that you won't get to this many stars instantly, but after further resets (such as eternity), when you come back to this challenge with more production, you might have to turn some autobuyers off to prestige with <span id="e198"></span> stars. In your second prestige, when the prestige formula is weaker (^<span id="e199"></span>), get <span id="e200"></span> stars and prestige. In your third prestige, when the prestige formula is normal (^<span id="e201"></span>), prestige at <span id="e202"></span> stars again. In your fourth prestige,  when the prestige formula is weaker (^<span id="e203"></span>), you won't be able to prestige again, but you should be able to finish the infinity challenge fairly quickly. This challenge takes <span id="e204"></span>, and with this strategy most of that is spent in the second prestige.</p>
    <p>The IC6 reward is actually decently strong, somewhat stronger than the IC1 or IC2 rewards were on completion. It won't speed up infinities as much, though, because of the IC4 reward still making long infinities better. Still, infinities should only be roughly <span id="e205"></span> to <span id="e206"></span> long until you unlock IC7, in <span id="e207"></span> or <span id="e208"></span> more infinities.</p>
    <p>Infinity Challenge 7: Easy. Prestige power is far more important than boosts, which is why this challenge is a nerf. This challenge doesn't require any special strategy, and takes roughly <span id="e209"></span>.</p>
    <p>The IC7 reward is fairly small; it's slightly larger than the IC5 reward was, but not much larger (it's roughly a <span id="e210"></span>x multiplier to normal generators). It's interesting to note that it actually gets smaller as you progress, not just in comparison to your stars but overall. Still, infinities should only be roughly <span id="e211"></span> long until you unlock IC8, in <span id="e212"></span> or <span id="e213"></span> more infinities.</p>
    <p>Infinity Challenge 8: Hard. This infinity challenge doesn't take too long but has strategy. First, turn all your autobuyers off, then manually buy <span id="e214"></span> each of Generator 1 through Generator 7, then buy max of Generator 8. Then, without turning autobuyers on yet, set autobuyers to buy singles of Generators 1 through Generator 7 and boosts, buy max of Generator 8, sacrifice off or set to some huge unreachable multiplier (like <span id="e215"></span>; the point of this is to not sacrifice at all, so either turning it off or setting it to a multiplier you'll never reach works), and prestige set to <span id="e216"></span>x multiplier. Then turn autobuyers on. Once you have <span id="e217"></span> IC8 purchases, set your non-prestige autobuyers as if you were playing normally, and either turn your prestige autobuyer off (prestige manually when progress slows down) or set it to <span id="e218"></span>. Alternatively, once you have <span id="e219"></span> IC8 purchases, set your non-prestige autobuyers as if you were playing normally, and set your prestige autobuyer to <span id="e220"></span>x. Either way, you should now be able to complete the challenge without using all your purchases, and without changing the prestige autobuyer. This challenge takes roughly <span id="e221"></span>. Remember to change your prestige autobuyer back to <span id="e222"></span>x after finishing the challenge. It's not clear if doing this challenge is actually worthwhile, given how close eternity is.</p>
    <p>The IC8 reward is roughly as strong as the IC7 reward. Infinities should only be roughly <span id="e223"></span> to <span id="e224"></span> long until you can eternity, in <span id="e225"></span> or <span id="e226"></span> more infinities.</p>
    <p>Unlike stars when you could infinity, IP don't cap at <span id="e227"></span>. However, getting enough more to get more than <span id="e228"></span> eternity points isn't worth it yet, so eternity for <span id="e229"></span> eternity points as soon as you can. You can get to this point from the start of infinity challenges in roughly <span id="e230"></span>.</p>
  </div>
  <div id="b23">
    <h3>Eternity to completing all eternity milestones</h3>
    <p>So, you've eternitied. This resets basically everything. You keep your slow autobuyers, and that's basically it. However, with your <span id="e231"></span> eternity points (EP) you can, and should, buy an Eternity Generator 1. Eternity generators (EGs) are like normal generators and infinity generators except that they cost eternity points. Eternity stars have two effects: a multiplier and a power. Note that you start with <span id="e232"></span> eternity stars at the start of each eternity. Eternity stars and eternity generators reset on eternity to the same extent infinity stars and infinity generators reset on infinity.</p>
    <p>Multiplier from eternity stars: (eternity stars)x.</p>
    <p>Power from eternity stars: <span id="e233"></span> + log<span id="e234"></span>(log<span id="e235"></span>(eternity stars)) / <span id="e236"></span></p>
    <p>You won't want to get more than <span id="e237"></span> EP per eternity for a while, but just for reference, here's the EP formula.</p>
    <p>EP formula: (total IP this eternity)^<span id="e238"></span></p>
    <p>The starting benefits from milestones are below, in the hopes that they will be convenient.</p>
    <p>Milestone formulas: <span id="e239"></span>^(min(<span id="e240"></span>, eternities)) starting stars, <span id="e241"></span>^(min(<span id="e242"></span>, eternities / <span id="e243"></span>)) starting IP, min(<span id="e244"></span>, eternities)^<span id="e245"></span> starting infinities</p>
    <p>The second eternity is much like the first, except far quicker, and generally following the guide above works. Following are the important differences, together with other important things to note.</p>
    <p>You should do your first infinity in Normal Challenge 12, because the condition does nothing and you'll get an autobuyer and a small multiplier for it. You don't need to unlock slow autobuyers again, since they're already unlocked. Normal Challenge 1 is comparatively harder, because the multiplier from eternity stars only applies to <span id="e246"></span> generator (albeit ^<span id="e247"></span>); you may thus want to do Normal Challenge 1 as a medium-difficulty challenge rather than an easy challenge, and do an extra normal infinity instead so you still have Infinity Generator 2 before starting the medium-difficulty challenges. Normal Challenge 2 is a tiny bit more annoying due to not being quicker by as much as the rest of the game is; you may want to do it last, and to do more normal infinities before doing it, but you will be able to buy things more often (every <span id="e248"></span> is fine). <span id="e249"></span> total infinities is enough to max the multiplier to normal generators from total IP, which helps for that. Right after breaking infinity, the best IP per infinity is somewhat higher; for example, <span id="e250"></span> IP on your first infinity after breaking infinity is reasonable. Don't forget to get <span id="e251"></span> infinities; this isn't a difference, but it's one of the easier things to forget because not doing it slows down progress rather than stopping it (these infinities will probably be far quicker than before, though, which is a difference). Infinity Challenge 1 doesn't require as much waiting before prestiging; <span id="e252"></span> should be more than enough. More generally, almost every infinity challenge is far quicker. For the sake of speed, it may be best to infinity and start an infinity challenge immediately after unlocking it rather than waiting for your infinity autobuyer's requirement.</p>
    <p>After Infinity Challenge 1, due to how quick infinities are, it's better to set prestige to <span id="e253"></span> than to <span id="e254"></span>x. However, note that whenever you set the prestige autobuyer or another reset autobuyer (such as the infinity autobuyer) based on time, if you go offline, ticks will be longer and so the autobuyer may trigger every few ticks, which may not let production build up enough. So if you go offline, you may want to adjust your reset autobuyers to trigger less often or instead be based on multiplier.</p>
    <p>Due to eternity stars, setting your infinity autobuyer to <span id="e255"></span>x best of last ten is good even just after Infinity Challenge 1, for the rest of the eternity. If you want, you can do slightly better manually early on by doing slightly longer infinities, because of how powerful Infinity Challenge 1 is (also note what was said above about starting an infinity challenge immediately after unlock). Infinity Challenge 4 is not far quicker; it's not worth doing and should be skipped. Because you start with <span id="e256"></span> stars, Infinity Challenge 5 doesn't have as much of a delay at the start of every prestige, so you can leave the prestige autobuyer at <span id="e257"></span> and it'll be fine. Infinity Challenge 8 is not far quicker because its speed depends on autobuyer speed, and definitely should be skipped. Make sure to buy a theorem (in the Studies tab) for <span id="e258"></span> stars and to buy another for <span id="e259"></span> IP; it's not crucial that you do this now, but you'll have to do it in one of the next <span id="e260"></span> eternities (counting this one) and there's no reason not to do it now. Generally, from now on, you should buy theorems with stars and IP as soon as they become affordable, even if this isn't stated explicitly.</p>
    <p>Overall, your second eternity can be as short as <span id="e261"></span> to <span id="e262"></span>.</p>
    <p>It is best to spend your next <span id="e263"></span> EP (including the <span id="e264"></span> you just got) on <span id="e265"></span> theorems, for <span id="e266"></span> EP and <span id="e267"></span> EP (it doesn't really matter whether you buy both theorems at once, or buy the first earlier and the second later). This will give you <span id="e268"></span> total theorems, which will let you buy Study 3, which will speed up eternities a lot. So don't buy Eternity Generator 1 again until you have <span id="e269"></span> total theorems.</p>
    <p>Your third eternity is a lot like the second, except that, from the <span id="e270"></span>-eternity eternity milestone, you start with all challenges (but not infinity challenges) completed, with all fast autobuyers, and with infinity broken, and since eternity generators are all multiplied by min(<span id="e271"></span>, eternities / <span id="e272"></span>), eternity stars will produce <span id="e273"></span>x as fast. The strategy is similar to that for second eternity, except that you don't need to do challenges, and there's thus no reason to do your first infinity in Normal Challenge 12. Remember to set your prestige autobuyer back to <span id="e274"></span>x until you complete IC1. You still want to do some early infinities for <span id="e275"></span> IP, perhaps until <span id="e276"></span> infinities and <span id="e277"></span> total IP. Once you're done with those early infinities, you can (though this is not strictly necessary) infinity a few times for <span id="e278"></span> to <span id="e279"></span> IP per infinity, then do more quick infinities to get up to <span id="e280"></span> infinities (infinity length will get down to roughly <span id="e281"></span> by the end of this). Infinity Challenge 5 now has basically no delay at the start of each prestige.</p>
    <p>Overall, your third eternity can be as short as <span id="e282"></span> to <span id="e283"></span>.</p>
    <p>Your fourth eternity is almost the same as the third, except that, from the <span id="e284"></span>-eternity eternity milestone, you can buy an Infinity Generator 1 before you infinity. Again, remember to set your prestige autobuyer back to <span id="e285"></span>x until you complete IC1. This eternity will be roughly the same length as the previous one.</p>
    <p>Now you can finally buy another theorem for <span id="e286"></span> EP and buy Study 3. This will make eternities a lot quicker. Getting <span id="e287"></span> infinities is now unnecessary. Also, the <span id="e288"></span>-eternity eternity milestone automatically completes ICs, which means you don't need to do them yourself and is thus very helpful. Initially it only completes the first <span id="e289"></span> ICs, so you might still have to do IC5 and IC7. You can set your prestige autobuyer to <span id="e290"></span> and your infinity autobuyer to <span id="e291"></span>x best of last ten, or try to slightly improve on this with manual prestige and infinity. You should still eternity for <span id="e292"></span> EP. This eternity should take roughly <span id="e293"></span> (maybe slightly quicker), mostly limited by autobuyers and (if you prestige and infinity manually) manual speed.</p>
    <p>Now keep doing eternities much like the last. The <span id="e294"></span>-eternity eternity milestone gives you some infinities (initially <span id="e295"></span>), which helps a bit but not that much. When you have <span id="e296"></span> eternities, you can (and should) get another EG1. The <span id="e297"></span>-eternity eternity milestone makes sacrifice not reset generators, which prevents some lag. It also lets you set the sacrifice autobuyer to <span id="e298"></span>x, as you should do. At this point, eternities are roughly <span id="e299"></span> long. The <span id="e300"></span>-eternity eternity milestone is just autobuyers (on by default) and thus is not much of a speedup. The <span id="e301"></span>-eternity eternity milestone lets you set the prestige autobuyer to prestige for a <span id="e302"></span>x multiplier, which is a very big speedup. You can also set the infinity autobuyer to infinity <span id="e303"></span> since total. (That is, set it to the value <span id="e304"></span> and the mode "Time since gain was total"; "Time since gain was total" is a helpful autobuyer mode that infinities some amount of time after gained IP reaches total IP.) You'll still need to buy infinity generators until you get autobuyers for them, though. Eternities should now be roughly <span id="e305"></span> to <span id="e306"></span> long. When you have <span id="e307"></span> eternities, you can, and should, buy EG2. After roughly <span id="e308"></span> to <span id="e309"></span> from <span id="e310"></span> eternities, you'll have <span id="e311"></span> eternities and thus will have completed all eternity milestones.</p>
  </div>
  <div id="b24">
    <h3>Completing all eternity milestones to unlocking the Eternity Producer</h3>
    <p>In this section of the game, you'll start to have several studies at once and to need to determine which studies are best. Generally, a multiplier to infinity generators is <span id="e312"></span> times better than the same multiplier to normal generators, and a multiplier to eternity generators is slightly better than (however many eternity generators you have any of) times better than the same multiplier to infinity generators. Of course, the studies that multiply normal generators generally have the biggest multipliers, and those that multiply eternity generators generally have the smallest multipliers, so determining which is best requires some mental arithemetic (and of course, multipliers should be compared logarithmically; a <span id="e313"></span>x multiplier is only <span id="e314"></span>x as good as a <span id="e315"></span>x multiplier to the same thing, since <span id="e316"></span> is <span id="e317"></span>^<span id="e318"></span>).</p>
    <p>First, turn off your eternity autobuyer. It's good in general, but there are advantages to doing a somewhat long eternity now. It gives less EP/second, but it makes Study 3 stronger and lets you get more theorems. Getting to <span id="e319"></span> IP should be enough to get another theorem with stars, get another theorem with IP, and noticeably increase Study 3's multiplier without taking too long (<span id="e320"></span> to <span id="e321"></span>), so do that. Note that you should buy the theorems with stars and IP as soon as you can afford them, as stated above. Then start doing quick eternities for <span id="e322"></span> EP again. In addition to this being efficient for IP/second, it makes EGs slightly stronger via more eternities, and gives you more starting benefits (in particular starting IP), which makes eternities even quicker.</p>
    <p>As for what to spend your EP on, first buy the first eternity upgrade once, then start saving for theorems with EP. After buying a theorem for <span id="e323"></span> EP and another theorem for <span id="e324"></span> EP, you can buy Study 4 to speed up quick eternities even more.</p>
    <p>At some point soon (you could do this immediately, or make it slightly faster by getting more eternities first), you should try to do another longer eternity to get more theorems. For this longer eternity, you'll want Studies 1 and 3, rather than 3 and 4, so respec your studies and buy Studies 1 and 3. You should be able to get <span id="e325"></span> more theorems with stars and also another theorem with infinity points, for <span id="e326"></span> total theorems, fairly quickly. After roughly <span id="e327"></span> (right before the second theorem bought with stars) you should switch the infinity autobuyer to <span id="e328"></span> since total, since IP gain will start to slow down. (Remember, this means to use the "Time since gain was total" mode, as explained at the end of the "Eternity to completing all eternity milestones" previous guide section.) Overall this eternity should take roughly <span id="e329"></span>. Remember to set your eternity autobuyer back to <span id="e330"></span> EP, and also you'll want to respec and buy Studies 3 and 4. Additionally, you can now set the infinity autobuyer to <span id="e331"></span>. Furthermore, soon you'll be able to buy another theorem for <span id="e332"></span> EP. Do so, and buy Study 1 (in addition to Studies 3 and 4, which you already have).</p>
    <p>Eternities are useful enough that you should try to get <span id="e333"></span> of them right now. They should only take roughly <span id="e334"></span> each. Buy EG2 again, then buy EG1 as it becomes affordable. From now on, advice about buying eternity upgrades and generators is similar to that about buying infinity upgrades and generators. The third and second upgrades start out good (the third especially so) but get worse per purchase; the first starts out bad but gets better per purchase (though it can only be purchased <span id="e335"></span> times, at which point its effect is ^<span id="e336"></span>, making the per-purchase eternity generator multiplier <span id="e337"></span>x).</p>
    <p>Eternities will start to be <span id="e338"></span> long once you have roughly <span id="e339"></span> of them. This makes it even easier to get to <span id="e340"></span> eternities.</p>
    <p>Once you have <span id="e341"></span> eternities, keep doing quick <span id="e342"></span>-EP eternities, and save EP to buy another theorem for <span id="e343"></span> EP. Once you can buy that theorem, buy it (giving you <span id="e344"></span> total theorems), and do another longer eternity with Studies 1, 2, and 3, and with your infinity autobuyer set to <span id="e345"></span>. As before, switch the infinity autobuyer to <span id="e346"></span> after <span id="e347"></span>. You should be able to, within roughly <span id="e348"></span> from the start of the eternity, buy another theorem with stars and <span id="e349"></span> more theorems with IP, for a total of <span id="e350"></span> theorems. You can now buy Study 4, so do that. Stay in this eternity until you can buy another theorem with stars, for a total of <span id="e351"></span> theorems.</p>
    <p>Now you can do slightly longer eternities for maximum EP/second. Set your infinity autobuyer to <span id="e352"></span> since total and your eternity autobuyer to <span id="e353"></span> EP. You should get roughly <span id="e354"></span> EP/second by doing this. Save EP for EG3 (<span id="e355"></span> EP), after buying which you should get <span id="e356"></span> EP/second, then for the first eternity upgrade for the second time (<span id="e357"></span> EP). Then buy all eternity generators costing up to <span id="e358"></span> EP in any order you want. By the end of this, you'll be getting roughly <span id="e359"></span> EP/second.</p>
    <p>Now save EP to buy another theorem with EP. After buying that theorem, do eternities for <span id="e360"></span> EP (and infinities for <span id="e361"></span> IP with the mode being amount) until you have <span id="e362"></span> eternities, to make Study 7 stronger. For these eternities, use Studies 3, 4, and 7. Each eternity should be roughly <span id="e363"></span> to <span id="e364"></span> long. With the EP you're getting, buy the second eternity upgrade (which is very good), then the first eternity upgrade (which is not as good), and then eternity generators as they become affordable.</p>
    <p>After these eternities, change the infinity autobuyer to <span id="e365"></span> since total, turn the eternity autobuyer off, and buy Studies 5, 6, and 7. You'll be doing another longer eternity, since longer eternities are now the best way to get more EP/second.</p>
    <p>You will soon get more than <span id="e366"></span> boosts and thus start producing boost power. Each boost reached in the current eternity above <span id="e367"></span> boosts (that is, max(0, boosts reached this eternity - <span id="e368"></span>) boosts)) produces <span id="e369"></span> boost power per second, so boost power gain is max(0, boosts reached this eternity - <span id="e370"></span>) * <span id="e371"></span>) per second. Losing boosts due to prestige or infinity does not decrease boost power production. Boost power resets on eternity (as does boost power production), but not on infinity. Boost power provides a multiplier to boosts based on its amount (<span id="e372"></span> + log<span id="e373"></span>(amount)). You also get theorems (which you keep on eternity) at certain thresholds of boost power. Boost power makes long eternities good and is eventually a major reason that they become better.</p>
    <p>Buy theorems with stars and IP as they become affordable. When you get <span id="e374"></span> total theorems, buy Study 8. Roughly <span id="e375"></span> after the start of the eternity, you should be able to eternity for <span id="e376"></span> EP. Do that, and buy the third eternity upgrade (which is at this point even better than EG4). If you have a small amount of extra EP, buy cheap eternity generators.</p>
    <p>Do another longer eternity, with the infinity autobuyer set to <span id="e377"></span> since total again. After roughly <span id="e378"></span>, you should be able to again eternity for <span id="e379"></span> EP. Do that, and buy EG4. Do another eternity for <span id="e380"></span> EP (which should take roughly <span id="e381"></span>), and buy the first eternity upgrade and another theorem for <span id="e382"></span> EP.</p>
    <p>In your next eternity, you should get <span id="e383"></span> EP, which will take roughly <span id="e384"></span>. During this eternity, you'll get another theorem with IP, for a total of <span id="e385"></span> theorems. Spend the EP you get on unlocking the Eternity Producer. You can reach this point roughly <span id="e386"></span> after getting all eternity milestones.</p>
    <p>Studies to use so far:</p>
    <table style="margin-left: auto; margin-right: auto;" style="width: 90%">
      <colgroup>
         <col span="1" style="width: 15%;">
         <col span="1" style="width: 15%;">
         <col span="1" style="width: 30%;">
         <col span="1" style="width: 30%;">
      </colgroup>
      <tr>
        <td style="text-align: center;">Total EP (roughly)</td>
        <td style="text-align: center;">Total theorems</td>
        <td style="text-align: center;">Studies</td>
        <td style="text-align: center;">Notes</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e387"></span></td>
        <td style="text-align: center;"><span id="e388"></span></td>
        <td style="text-align: center;">3</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e389"></span></td>
        <td style="text-align: center;"><span id="e390"></span></td>
        <td style="text-align: center;">3, 4</td>
        <td style="text-align: center;">For quick eternities</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e391"></span></td>
        <td style="text-align: center;"><span id="e392"></span></td>
        <td style="text-align: center;">1, 3</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e393"></span></td>
        <td style="text-align: center;"><span id="e394"></span></td>
        <td style="text-align: center;">1, 3, 4</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e395"></span></td>
        <td style="text-align: center;"><span id="e396"></span></td>
        <td style="text-align: center;">1, 2, 3</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e397"></span></td>
        <td style="text-align: center;"><span id="e398"></span></td>
        <td style="text-align: center;">1, 2, 3, 4</td>
        <td style="text-align: center;">In same eternity as previous</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e399"></span></td>
        <td style="text-align: center;"><span id="e400"></span></td>
        <td style="text-align: center;">3, 4, 7</td>
        <td style="text-align: center;">For short eternities (2 EP each)</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e401"></span></td>
        <td style="text-align: center;"><span id="e402"></span></td>
        <td style="text-align: center;">5, 6, 7</td>
        <td style="text-align: center;">After <span id="e403"></span> eternities</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e404"></span></td>
        <td style="text-align: center;"><span id="e405"></span></td>
        <td style="text-align: center;">5, 6, 7, 8</td>
        <td style="text-align: center;">In same eternity as previous</td>
      </tr>
    </table>
  </div>
  <div id="b25">
    <h3>Unlocking the Eternity Producer to starting Eternity Challenge 1</h3>
    <p>The Eternity Producer produces eternities, and gives a multiplier to eternity generators based on their amount. Upgrades for it (to produce more eternities and increase the multiplier) are generally fairly minor: worse than an eternity upgrade with the same cost, but better than an eternity generator. Note that with more eternities (from, for example, waiting overnight), progress will be significantly faster and the time it takes to do things after getting a large number of additional eternities will likely be less than the time given below.</p>
    <p>Do another long eternity (roughly <span id="e406"></span>) to get another theorem with stars and another extra theorem from boost power, increasing your total theorems to <span id="e407"></span>. As before, set the infinity autobuyer to <span id="e408"></span> since total. Now do an eternity (roughly <span id="e409"></span> long) for <span id="e410"></span> EP with Studies 5, 6, 8, and 10. Buy the second eternity upgrade (rather than the first). At this point, you should replace Study 10 with Study 9 instead. Do another eternity for <span id="e411"></span> EP, which should take roughly <span id="e412"></span>, and buy the first eternity upgrade. Do another eternity for <span id="e413"></span> EP, which should take roughly <span id="e414"></span>, and buy EG5.</p>
    <p>From now on, you can choose when to do eternities yourself. Generally try to get between <span id="e415"></span>x and <span id="e416"></span>x your total EP in each eternity, with smaller multipliers like <span id="e417"></span>x generally being better early and larger multipliers like <span id="e418"></span>x generally being better late. If you're about to be able to get a theorem, wait for it. Generally, almost all eternities should be less than <span id="e419"></span>.</p>
    <p>Once you have <span id="e420"></span> theorems, you should switch to using Studies 3, 5, 6, 7, and 8 (that is, losing 9 and getting 3 and 7); you can afford them now, and 3 and 7 are each almost as strong as 9 is. (You'll get <span id="e421"></span> theorems when you buy the theorem costing <span id="e422"></span> EP, unless you've already gotten another theorem from boost power.) While trying to get <span id="e423"></span> EP (or, slightly earlier, <span id="e424"></span> EP), there's a small wall and so you'll probably need to do a long eternity (<span id="e425"></span>); during this eternity you should be able to get a theorem for <span id="e426"></span> boost power, perhaps by making the eternity somewhat longer (<span id="e427"></span>). Getting this theorem (and the theorem for <span id="e428"></span> EP) will let you buy Study 9 in addition to Studies 5, 6, 7, and 8, instead of Study 3; Study 9 is somewhat better than Study 3 at this point, so this is good. After roughly <span id="e429"></span> EP, eternities should become a lot faster than they were immediately before (they should now be <span id="e430"></span> to <span id="e431"></span> long), and you should be able to get as far as buying the second eternity upgrade for <span id="e432"></span> EP in roughly <span id="e433"></span>. Once you buy the second eternity upgrade for <span id="e434"></span> EP, you should do an eternity with Studies 5, 6, 8, and 9 and unlock Eternity Challenge 1 when possible. After unlocking Eternity Challenge 1, start it. You can reach this point in roughly <span id="e435"></span> from unlocking the Eternity Producer.</p>
    <p> The next section of the guide becomes visible when you complete Eternity Challenge 1 for the first time, so information on how to do so is in this section (it is also repeated in the next section).</p>
    <p>Eternity challenges (or ECs) are somewhat like challenges and infinity challenges. There are several important differences, however. Eternity challenges require a certain amount of IP to eternity and complete the challenge, rather than a certain amount of stars to infinity and complete the challenge. They have infinity-challenge-like rewards that make various things stronger, but they can each be completed up to <span id="e436"></span> times, having a higher goal amount of IP each time and getting a stronger reward for each time completed. Finally, they have a requirement (depending on times completed) and a cost in theorems (fixed for each challenge) to unlock, and must be explicitly unlocked to be entered. Note that you can respec studies in an eternity challenge if you want. You will get the theorems you paid to unlock an eternity challenge back when you complete it or respec your eternity challenge (which will lock it again).</p>
    <p>To recap, you can do EC1 the first time (EC1x1) at <span id="e437"></span> EP, unlocking it with Studies 5, 6, 8, and 9. Once you unlock it, respec your studies and buy Studies 3, 8, 10, and 12. Within EC1x1, you should infinity for <span id="e438"></span>x best of last ten rather than, for example, every <span id="e439"></span>. This challenge should take roughly <span id="e440"></span> to <span id="e441"></span> to complete.</p>
    <p>Studies to use in this phase:</p>
    <table style="margin-left: auto; margin-right: auto;" style="width: 90%">
      <colgroup>
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 30%;">
         <col span="1" style="width: 30%;">
      </colgroup>
      <tr>
        <td style="text-align: center;">Total EP (roughly)</td>
        <td style="text-align: center;">Total theorems</td>
        <td style="text-align: center;">Eternity Challenge</td>
        <td style="text-align: center;">Studies</td>
        <td style="text-align: center;">Notes</td>
      </tr>
      <tr>
        <tr>
          <td style="text-align: center;"><span id="e442"></span></td>
          <td style="text-align: center;"><span id="e443"></span></td>
          <td/>
          <td style="text-align: center;">5, 6, 7, 8</td>
          <td/>
        </tr>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e444"></span></td>
        <td style="text-align: center;"><span id="e445"></span></td>
        <td/>
        <td style="text-align: center;">5, 6, 8, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e446"></span></td>
        <td style="text-align: center;"><span id="e447"></span></td>
        <td/>
        <td style="text-align: center;">5, 6, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e448"></span></td>
        <td style="text-align: center;"><span id="e449"></span></td>
        <td/>
        <td style="text-align: center;">3, 5, 6, 7, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e450"></span></td>
        <td style="text-align: center;"><span id="e451"></span></td>
        <td/>
        <td style="text-align: center;">5, 6, 7, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e452"></span></td>
        <td style="text-align: center;"><span id="e453"></span></td>
        <td style="text-align: center;">EC1x1</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9<br/>complete 3, 8, 10, 12</td>
        <td/>
      </tr>
    </table>
  </div>
  <div id="b26">
    <h3>Starting Eternity Challenge 1 to unlocking chroma</h3>
    <p>Eternity challenges (or ECs) are somewhat like challenges and infinity challenges. There are several important differences, however. Eternity challenges require a certain amount of IP to eternity and complete the challenge, rather than a certain amount of stars to infinity and complete the challenge. They have infinity-challenge-like rewards that make various things stronger, but they can each be completed up to <span id="e454"></span> times, having a higher goal amount of IP each time and getting a stronger reward for each time completed. Finally, they have a requirement (depending on times completed) and a cost in theorems (fixed for each challenge) to unlock, and must be explicitly unlocked to be entered. Note that you can respec studies in an eternity challenge if you want. You will get the theorems you paid to unlock an eternity challenge back when you complete it or respec your eternity challenge (which will lock it again).</p>
    <p>To recap, you can do EC1 the first time (EC1x1) at <span id="e455"></span> EP, unlocking it with Studies 5, 6, 8, and 9. Once you unlock it, respec your studies and buy Studies 3, 8, 10, and 12. Within EC1x1, you should infinity for <span id="e456"></span>x best of last ten rather than, for example, every <span id="e457"></span>. This challenge should take roughly <span id="e458"></span> to <span id="e459"></span> to complete.</p>
    <p>Switch back to infinities that are <span id="e460"></span> long and Studies 5, 6, 7, 8, and 9 after completing EC1x1. You should be able to get <span id="e461"></span> EP and buy EG8 with it in an eternity between <span id="e462"></span> and <span id="e463"></span> long. EG8 will make eternities somewhat faster (<span id="e464"></span>). When (slightly later) you get <span id="e465"></span> total theorems, replace Study 7 by Study 10, making your studies be 5, 6, 8, 9, and 10. Once you get roughly <span id="e466"></span> EP, you can do EC2x1 (EC2 for the first time). Unlock it with Studies 5, 6, 7, 8, and 9, and complete it with Studies 6, 8, 9, and 10. Unlocking and completing it should each take less than <span id="e467"></span>. After completing EC2x1, switch back to Studies 5, 6, 8, 9, and 10. At this point, your eternities should generally be for between <span id="e468"></span>x and <span id="e469"></span>x total EP. Getting <span id="e470"></span> EP is somewhat hard (it requires an eternity that is <span id="e471"></span> long), but once you get that much EP you can do EC1x2 (EC1 for the second time). Unlock with 5, 6, 7, 8, 9 (which should take roughly <span id="e472"></span>), and complete with 8, 10, 11, and 12 (if you already have <span id="e473"></span> eternities, you can use 8, 9, 10, and 12 instead and thus not have to wait for 11 to build up). As before, infinity for <span id="e474"></span>x best of last ten within EC1x2. EC1x2 will take roughly <span id="e475"></span> to complete.</p>
    <p>Next, for maximum speed, you should actually do EC4x1. EC3x1 has a slightly lower unlock requirement and cost than EC4x1, but is significantly harder (though both have similar requirements for completion). I do regret that EC4x1 comes before EC3x1, though in general completion x of EC4 is harder than completion x of EC3. For EC4x1, you should get <span id="e476"></span> total EP (via a eternity roughly <span id="e477"></span> long), and unlock and complete with 5, 6, 7, 8, 9. When doing EC4x1, wait <span id="e478"></span> before your first infinity to let boost power and eternity stars build up, and then do infinities that are <span id="e479"></span> long. You should easily be able to complete EC4x1 in roughly <span id="e480"></span>. Then do EC3x1. Unlock with 5, 6, 7, 8, 9, and complete with 3, 8, 9, 12. Infinity for <span id="e481"></span>x best of last ten within EC3x1. EC3x1 should take at most roughly <span id="e482"></span>, though it is faster if you have more eternities; it will take only <span id="e483"></span> to <span id="e484"></span> if you have <span id="e485"></span> eternities.</p>
    <p>After doing EC3x1 and EC4x1 (whatever order you do them in), you'll have a burst of progress; it's now better to do eternities for <span id="e486"></span>x to <span id="e487"></span>x in general, though your first eternity after EC3x1 and EC4x1 might give you even more EP than that (your eternities should be at least <span id="e488"></span> long). At roughly <span id="e489"></span> total EP (at which point progress should still be rather fast, with eternities lasting less than <span id="e490"></span>) do EC1x3, unlock 5, 6, 8, 9, 10, complete 3, 8, 9, 10, 12, infinity autobuyer <span id="e491"></span>x. EC1x3 should take roughly <span id="e492"></span>. With some eternities <span id="e493"></span> to <span id="e494"></span> in length (the later ones being longer), you should be able to get to <span id="e495"></span> total theorems at roughly <span id="e496"></span> EP, at which point you can buy Study 7. Once you get <span id="e497"></span> EP, do EC1x4, unlock 5, 6, 8, 9, 10, complete 3, 8, 9, 10, 12, infinity <span id="e498"></span>x. EC1x4 should take <span id="e499"></span> to <span id="e500"></span>. Next, before getting more EP, do EC3x2, unlock 5, 6, 8, 9, 10, complete 3, 7, 8, 9, 12, infinity <span id="e501"></span>x. EC3x2 should take <span id="e502"></span> to <span id="e503"></span>. In general, even-numbered ECs are harder than odd-numbered ECs, which is why EC3x2 can be done before EC2x2. You will now have <span id="e504"></span> eternity challenge completions, which will allow you to produce boost power faster.</p>
    <p>After doing EC1x4 and EC3x2, you'll have another burst of progress; your first eternity might give you <span id="e505"></span>x EP in <span id="e506"></span>. In fact, eternities from now on will often take only <span id="e507"></span>. Once you get <span id="e508"></span> EP, do EC2x2, unlock 5, 6, 8, 9, 10, complete 6, 8, 9, 10, 12. It should take only <span id="e509"></span> to complete; it's only being done now as opposed to earlier because progress was so fast. You should now have <span id="e510"></span> total theorems; replace Study 7 by Study 12, for 5, 6, 8, 9, 10, 12. At roughly <span id="e511"></span> EP (you might need an eternity <span id="e512"></span> long to get this much EP), do EC3x3, unlock 5, 6, 8, 9, 10, complete 3, 7, 8, 9, 12, infinity <span id="e513"></span>x. The production of boost power helps a lot in this challenge. EC3x3 should take <span id="e514"></span> to <span id="e515"></span>. At this point, eternities will get somewhat longer, getting as long as <span id="e516"></span> to <span id="e517"></span> before you get <span id="e518"></span> EP. When you get <span id="e519"></span> EP, you can do EC4x2, unlock (<span id="e520"></span>) and complete (<span id="e521"></span>) 1, 2, 3, 5, 6, 8, (for completion) first <span id="e522"></span> infinities for <span id="e523"></span> and <span id="e524"></span> IP (each roughly <span id="e525"></span>), following infinities <span id="e526"></span>. When you get <span id="e527"></span> EP, do EC2x3, unlock 5, 6, 8, 9, 10, 12, complete 2, 3, 6, 8, 9, 10 (<span id="e528"></span>). When you get <span id="e529"></span> EP, do EC3x4, unlock 5, 6, 8, 9, 10, 12, complete 3, 4, 7, 8, 9, 12 (<span id="e530"></span>).</p>
    <p>After EC3x4, change your studies to 1, 2, 3, 5, 6, 8, 9. At this point, progress is so fast that you may want to do eternities <span id="e531"></span> long if you can gain <span id="e532"></span>x EP with them; from this point on, every eternity challenge completion will be a rather large benefit to progress, and progress will slow down somewhat directly before the next eternity challenge completion. At <span id="e533"></span> EP, do EC2x4, unlock 1, 3, 5, 6, 8, 9 (<span id="e534"></span>), complete 3, 6, 8, 9, 10, 12 (<span id="e535"></span>). At <span id="e536"></span> EP, do EC5x1, unlock 1, 3, 5, 6, 8, 9, complete 1, 2, 3, 4, 5, 6, 8 (<span id="e537"></span>). At <span id="e538"></span> EP, do EC6x1, unlock whatever (you have the unlock requirement already), complete 3, 5, 6, 8, 9, 10 (<span id="e539"></span>). You can get here within roughly <span id="e540"></span> from starting EC1x1.</p>
    <p>After EC6x1, you'll have <span id="e541"></span> EC completions, which will give a huge multiplier (<span id="e542"></span>x initially) to eternity gain. You'll soon (in <span id="e543"></span> to <span id="e544"></span>) be able to gain <span id="e545"></span> permanence (or slightly more). Do so. Your first priority should be getting permanence quicker, so get the first permanence upgrade so that you can get permanence <span id="e546"></span>x faster. When you can next get <span id="e547"></span> permanence in roughly <span id="e548"></span>, get the fourth permanence upgrade so you can get permanence roughly <span id="e549"></span>x faster. Then get <span id="e550"></span> permanence (which takes roughly <span id="e551"></span>) and buy the second and third permanence upgrades. While you're waiting for permanence, you can gain some EP. After buying all the permanence upgrades for the first time, you can wait to gain permanence until you can gain enough to buy each upgrade once; it's unclear if this is the most efficient thing to do but it's easier than gaining permanence more frequently. Roughly <span id="e552"></span> after buying all the permanence upgrades for the first time, you should be able to get <span id="e553"></span> EP and <span id="e554"></span> total theorems. When you do, do EC4x3, unlock and complete 1, 2, 3, 5, 6, 8, 9, infinity <span id="e555"></span>. EC4x3 should be very easy. When you get a theorem for <span id="e556"></span> EP giving you <span id="e557"></span> total theorems, buy Study 4, making your studies be 1, 2, 3, 4, 5, 6, 8, 9. Once you buy each permanence upgrade <span id="e558"></span> times (so the cost of each is <span id="e559"></span> permanence), switch your studies to 1, 5, 6, 8, 9, 10, 12; this is better now since the third permanence upgrade is making third-row studies stronger.</p>
    <p>Once you get <span id="e560"></span> EP, at which point you should have <span id="e561"></span> theorems and current permanence upgrade costs should be at least <span id="e562"></span> per upgrade, do EC5x2, unlock and complete 1, 2, 3, 5, 6, 8, 9 (completing takes <span id="e563"></span>). Once you get <span id="e564"></span> EP, with permanence upgrade costs at least <span id="e565"></span>, do EC7x1, unlock whatever, complete 5, 6, 8, 9, 10, 12 (<span id="e566"></span>). Once you get <span id="e567"></span> EP,  with permanence upgrade costs at least <span id="e568"></span>, do EC5x3, unlock and complete 1, 3, 5, 6, 8, 9, 10 (this isn't optimal for unlocking but unlocking is very easy so it doesn't matter, completing takes <span id="e569"></span>). Once you get <span id="e570"></span> theorems, buy Study 7, to make your studies be 1, 5, 6, 7, 8, 9, 10, 12. Once you get <span id="e571"></span> EP, with permanence upgrade costs at least <span id="e572"></span>, do EC6x2, unlock whatever, complete 5, 6, 8, 9, 10, 11, 12 (<span id="e573"></span>). Once you get <span id="e574"></span> total theorems, replace Study 7 by Study 2, to make your studies be 1, 2, 5, 6, 8, 9, 10, 12. Once you get <span id="e575"></span> EP, with permanence upgrade costs at least <span id="e576"></span>, do EC5x4, unlock and complete 1, 3, 5, 6, 8, 9, 10 (both quick). Once you can unlock EC7x2 (<span id="e577"></span> EP), with permanence upgrade costs at least <span id="e578"></span>, do EC7x2, unlock whatever, complete 5, 6, 8, 9, 10, 11, 12 (<span id="e579"></span>). At roughly <span id="e580"></span> EP, replace Study 2 by Study 11 (because eternities are longer than they were before), to make your studies be 1, 5, 6, 8, 9, 10, 11, 12. At this point, since you have Study 11, it's reasonable to do longer eternities that still gain a lot of EP, such as, for example, an eternity <span id="e581"></span> long for <span id="e582"></span>x EP. Once you have <span id="e583"></span> EP (permanence upgrade costs will probably be at least <span id="e584"></span> but it doesn't matter), do EC8x1, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (<span id="e585"></span>).</p>
    <p>You now have <span id="e586"></span> EC completions and gain IP without needing to infinity, so you can turn your infinity autobuyer off. You can also now view the chroma tab, but it won't be useful for a while. Do EC4x4, unlock and complete whatever (EC4x4 is so easy that you don't need any studies). Replace Study 11 by Study 2 again, since now that you don't need to infinity eternities are shorter (your first few eternities after completing EC8x1 and EC4x4 can be less than <span id="e587"></span>), making your studies be 1, 2, 5, 6, 8, 9, 10, 12. At roughly <span id="e588"></span> EP, however, eternities get long enough that it is again better to replace Study 2 by Study 11, making your studies be 1, 5, 6, 8, 9, 10, 11, 12. Once you get <span id="e589"></span> EP, with permanence upgrade costs at least <span id="e590"></span>, do EC6x3, unlock whatever, complete 5, 6, 8, 9, 10, 11, 12 (<span id="e591"></span>). Replace Study 11 by Study 2, because eternities are quick. Once you get <span id="e592"></span> EP (which should take at most <span id="e593"></span>), with permanence upgrade costs at least <span id="e594"></span> (as before), do EC7x3, unlock whatever, complete 3, 5, 6, 8, 9, 10, 12 (less than <span id="e595"></span>). At roughly <span id="e596"></span> EP, switch back from Study 2 to Study 11 because eternities are longer. If you don't have the theorem requiring <span id="e597"></span> boost power yet, this is a good place to get it; it's fairly quick to get and it helps a little. Once you get <span id="e598"></span> EP, with permanence upgrade costs at least <span id="e599"></span>, do EC7x4, unlock whatever, complete 3, 5, 6, 8, 9, 10, 12 (<span id="e600"></span>). You should now have <span id="e601"></span> total theorems. Switch your studies to 1, 2, 3, 5, 6, 8, 9, 10, 12. When you get <span id="e602"></span> total theorems, switch to 1, 2, 5, 6, 8, 9, 10, 11, 12 because eternities are getting longer and you can afford it. Once you get <span id="e603"></span> EP, do EC8x2, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (<span id="e604"></span>).</p>
    <p>Fairly soon, you should get enough EP (<span id="e605"></span> EP) to unlock chroma. Do it. You should have completed all ECs 4 times, except for EC6 (3 times) and EC8 (2 times). You can get here in roughly <span id="e606"></span> from having <span id="e607"></span> EC completions, or <span id="e608"></span> from starting EC1x1.</p>
    <p>Studies to use in this phase:</p>
    <table style="margin-left: auto; margin-right: auto;" style="width: 90%">
      <colgroup>
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 25%;">
         <col span="1" style="width: 25%;">
      </colgroup>
      <tr>
        <td style="text-align: center;">Total EP (roughly)</td>
        <td style="text-align: center;">Total theorems</td>
        <td style="text-align: center;">Permanence upgrade costs</td>
        <td style="text-align: center;">Eternity Challenge</td>
        <td style="text-align: center;">Studies</td>
        <td style="text-align: center;">Notes</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e609"></span></td>
        <td style="text-align: center;"><span id="e610"></span></td>
        <td/>
        <td/>
        <td style="text-align: center;">5, 6, 7, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e611"></span></td>
        <td style="text-align: center;"><span id="e612"></span></td>
        <td/>
        <td style="text-align: center;">EC1x1</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9<br/>complete 3, 8, 10, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e613"></span>倍</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e614"></span></td>
        <td style="text-align: center;"><span id="e615"></span></td>
        <td/>
        <td/>
        <td style="text-align: center;">5, 6, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e616"></span></td>
        <td style="text-align: center;"><span id="e617"></span></td>
        <td/>
        <td style="text-align: center;">EC2x1</td>
        <td style="text-align: center;">unlock 5, 6, 7, 8, 9<br/>complete 6, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e618"></span></td>
        <td style="text-align: center;"><span id="e619"></span></td>
        <td/>
        <td style="text-align: center;">EC1x2</td>
        <td style="text-align: center;">unlock 5, 6, 7, 8, 9<br/>complete 8, 10, 11, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e620"></span>x, takes <span id="e621"></span>, complete with 8, 9, 10, 12 if you have <span id="e622"></span> eternities</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e623"></span></td>
        <td style="text-align: center;"><span id="e624"></span></td>
        <td/>
        <td style="text-align: center;">EC4x1</td>
        <td style="text-align: center;">unlock and complete 5, 6, 7, 8, 9</td>
        <td style="text-align: center;">First infinity <span id="e625"></span>, then <span id="e626"></span></td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e627"></span></td>
        <td style="text-align: center;"><span id="e628"></span></td>
        <td/>
        <td style="text-align: center;">EC3x1</td>
        <td style="text-align: center;">unlock 5, 6, 7, 8, 9<br/>complete 3, 8, 9, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e629"></span>x, gets faster with more eternities</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e630"></span></td>
        <td style="text-align: center;"><span id="e631"></span></td>
        <td/>
        <td style="text-align: center;">EC1x3</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10<br/>complete 3, 8, 9, 10, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e632"></span>倍</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e633"></span></td>
        <td style="text-align: center;"><span id="e634"></span></td>
        <td/>
        <td/>
        <td style="text-align: center;">5, 6, 7, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e635"></span></td>
        <td style="text-align: center;"><span id="e636"></span></td>
        <td/>
        <td style="text-align: center;">EC1x4</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10<br/>complete 3, 8, 9, 10, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e637"></span>倍</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e638"></span></td>
        <td style="text-align: center;"><span id="e639"></span></td>
        <td/>
        <td style="text-align: center;">EC3x2</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10<br/>complete 3, 7, 8, 9, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e640"></span>倍</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e641"></span></td>
        <td style="text-align: center;"><span id="e642"></span></td>
        <td/>
        <td style="text-align: center;">EC2x2</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10<br/>complete 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e643"></span></td>
        <td style="text-align: center;"><span id="e644"></span></td>
        <td/>
        <td/>
        <td style="text-align: center;">5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e645"></span></td>
        <td style="text-align: center;"><span id="e646"></span></td>
        <td/>
        <td style="text-align: center;">EC3x3</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10<br/>complete 3, 7, 8, 9, 12</td>
        <td style="text-align: center;">Infinity autobuyer <span id="e647"></span>倍</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e648"></span></td>
        <td style="text-align: center;"><span id="e649"></span></td>
        <td/>
        <td style="text-align: center;">EC4x2</td>
        <td style="text-align: center;">unlock and complete 1, 2, 3, 5, 6, 8</td>
        <td style="text-align: center;">Unlock is slow for an EC unlock (<span id="e650"></span>), first <span id="e651"></span> infinities <span id="e652"></span>, then <span id="e653"></span></td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e654"></span></td>
        <td style="text-align: center;"><span id="e655"></span></td>
        <td/>
        <td style="text-align: center;">EC2x3</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10, 12<br/>complete 2, 3, 6, 8, 9, 10 </td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e656"></span></td>
        <td style="text-align: center;"><span id="e657"></span></td>
        <td/>
        <td style="text-align: center;">EC3x4</td>
        <td style="text-align: center;">unlock 5, 6, 8, 9, 10, 12<br/>complete 3, 4, 7, 8, 9, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e658"></span></td>
        <td style="text-align: center;"><span id="e659"></span></td>
        <td/>
        <td/>
        <td style="text-align: center;">1, 2, 3, 5, 6, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e660"></span></td>
        <td style="text-align: center;"><span id="e661"></span></td>
        <td/>
        <td style="text-align: center;">EC2x4</td>
        <td style="text-align: center;">unlock 1, 3, 5, 6, 8, 9<br/>complete 3, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e662"></span></td>
        <td style="text-align: center;"><span id="e663"></span></td>
        <td/>
        <td style="text-align: center;">EC5x1</td>
        <td style="text-align: center;">unlock 1, 3, 5, 6, 8, 9<br/>complete 1, 2, 3, 4, 5, 6, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e664"></span></td>
        <td style="text-align: center;"><span id="e665"></span></td>
        <td/>
        <td style="text-align: center;">EC6x1</td>
        <td style="text-align: center;">unlock whatever<br/>complete 3, 5, 6, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e666"></span></td>
        <td style="text-align: center;"><span id="e667"></span></td>
        <td style="text-align: center;"><span id="e668"></span></td>
        <td style="text-align: center;">EC4x3</td>
        <td style="text-align: center;">unlock and complete 1, 2, 3, 5, 6, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e669"></span></td>
        <td style="text-align: center;"><span id="e670"></span></td>
        <td style="text-align: center;"><span id="e671"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 3, 4, 5, 6, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e672"></span></td>
        <td style="text-align: center;"><span id="e673"></span></td>
        <td style="text-align: center;"><span id="e674"></span></td>
        <td/>
        <td style="text-align: center;">1, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e675"></span></td>
        <td style="text-align: center;"><span id="e676"></span></td>
        <td style="text-align: center;"><span id="e677"></span></td>
        <td style="text-align: center;">EC5x2</td>
        <td style="text-align: center;">unlock and complete 1, 2, 3, 5, 6, 8, 9</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e678"></span></td>
        <td style="text-align: center;"><span id="e679"></span></td>
        <td style="text-align: center;"><span id="e680"></span></td>
        <td style="text-align: center;">EC7x1</td>
        <td style="text-align: center;">unlock whatever<br/>complete 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e681"></span></td>
        <td style="text-align: center;"><span id="e682"></span></td>
        <td style="text-align: center;"><span id="e683"></span></td>
        <td style="text-align: center;">EC5x3</td>
        <td style="text-align: center;">unlock and complete 1, 3, 5, 6, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e684"></span></td>
        <td style="text-align: center;"><span id="e685"></span></td>
        <td style="text-align: center;"><span id="e686"></span></td>
        <td/>
        <td style="text-align: center;">1, 5, 6, 7, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e687"></span></td>
        <td style="text-align: center;"><span id="e688"></span></td>
        <td style="text-align: center;"><span id="e689"></span></td>
        <td style="text-align: center;">EC6x2</td>
        <td style="text-align: center;">unlock whatever<br/>complete 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e690"></span></td>
        <td style="text-align: center;"><span id="e691"></span></td>
        <td style="text-align: center;"><span id="e692"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e693"></span></td>
        <td style="text-align: center;"><span id="e694"></span></td>
        <td style="text-align: center;"><span id="e695"></span></td>
        <td style="text-align: center;">EC5x4</td>
        <td style="text-align: center;">unlock and complete 1, 3, 5, 6, 8, 9, 10</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e696"></span></td>
        <td style="text-align: center;"><span id="e697"></span></td>
        <td style="text-align: center;"><span id="e698"></span></td>
        <td style="text-align: center;">EC7x2</td>
        <td style="text-align: center;">unlock whatever<br/>complete 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e699"></span></td>
        <td style="text-align: center;"><span id="e700"></span></td>
        <td style="text-align: center;"><span id="e701"></span></td>
        <td/>
        <td style="text-align: center;">1, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e702"></span></td>
        <td style="text-align: center;"><span id="e703"></span></td>
        <td style="text-align: center;"><span id="e704"></span></td>
        <td style="text-align: center;">EC8x1</td>
        <td style="text-align: center;">unlock 9, 10, 11, 12<br/>complete 1, 2, 3, 4, 5, 6, 7, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e705"></span></td>
        <td style="text-align: center;"><span id="e706"></span></td>
        <td style="text-align: center;"><span id="e707"></span></td>
        <td style="text-align: center;">EC4x4</td>
        <td style="text-align: center;">unlock and complete whatever</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e708"></span></td>
        <td style="text-align: center;"><span id="e709"></span></td>
        <td style="text-align: center;"><span id="e710"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e711"></span></td>
        <td style="text-align: center;"><span id="e712"></span></td>
        <td style="text-align: center;"><span id="e713"></span></td>
        <td/>
        <td style="text-align: center;">1, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e714"></span></td>
        <td style="text-align: center;"><span id="e715"></span></td>
        <td style="text-align: center;"><span id="e716"></span></td>
        <td style="text-align: center;">EC6x3</td>
        <td style="text-align: center;">unlock whatever<br/>complete 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e717"></span></td>
        <td style="text-align: center;"><span id="e718"></span></td>
        <td style="text-align: center;"><span id="e719"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e720"></span></td>
        <td style="text-align: center;"><span id="e721"></span></td>
        <td/>
        <td style="text-align: center;">EC7x3</td>
        <td style="text-align: center;">unlock whatever<br/>complete 3, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e722"></span></td>
        <td style="text-align: center;"><span id="e723"></span></td>
        <td style="text-align: center;"><span id="e724"></span></td>
        <td/>
        <td style="text-align: center;">1, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e725"></span></td>
        <td style="text-align: center;"><span id="e726"></span></td>
        <td style="text-align: center;"><span id="e727"></span></td>
        <td style="text-align: center;">EC7x4</td>
        <td style="text-align: center;">unlock whatever<br/>complete 3, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e728"></span></td>
        <td style="text-align: center;"><span id="e729"></span></td>
        <td style="text-align: center;"><span id="e730"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 3, 5, 6, 8, 9, 10, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e731"></span></td>
        <td style="text-align: center;"><span id="e732"></span></td>
        <td style="text-align: center;"><span id="e733"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e734"></span></td>
        <td style="text-align: center;"><span id="e735"></span></td>
        <td style="text-align: center;"><span id="e736"></span></td>
        <td style="text-align: center;">EC8x2</td>
        <td style="text-align: center;">unlock 9, 10, 11, 12<br/>complete 1, 2, 3, 4, 5, 6, 7, 8</td>
        <td/>
      </tr>
    </table>
  </div>
  <div id="b27">
    <h3>Unlocking chroma to complexity</h3>
    <p>Chroma works as follows. Chroma builds up over time in an eternity and resets on eternity, getting <span id="e737"></span> times closer to the cap every (cap / (<span id="e738"></span> * buildup speed)) seconds. Alternatively, as a formula, chroma is given below.</p>
    <p>chroma = cap * (<span id="e739"></span> - <span id="e740"></span> * <span id="e741"></span>^(-time in eternity * buildup speed / cap)).</p>
    <p>Since chroma builds up over an eternity, it is best to wait for it to build up when you unlock it, though you can gain permanence while waiting. In the eternity that you unlock it, you should try to get <span id="e742"></span> chroma and thus <span id="e743"></span> grey. This will take roughly <span id="e744"></span>. After this, you should be able to do quick eternities each gaining you a lot of EP, and it is thus best to replace Study 11 by Study 3, making your studies be 1, 2, 3, 5, 6, 8, 9, 10, 12. At roughly <span id="e745"></span> EP, it's best to switch back to Study 11. Only a few eternities later, at <span id="e746"></span> EP, it's best to do a long eternity for some additional grey. You should try to get <span id="e747"></span> grey, which will take roughly <span id="e748"></span>. After that, keep gaining more EP. Once you get <span id="e749"></span> EP, do EC8x3, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (<span id="e750"></span>). Then do EC6x4, unlock and complete whatever (it's so easy to complete that you don't need any studies).</p>
    <p>You should soon be able to get <span id="e751"></span> EP to unlock purple, without any very long eternities. Unlock purple, start producing purple, and do an eternity long enough to let you get <span id="e752"></span> purple (which should take roughly <span id="e753"></span>). Note that from here on, specific amounts of colors to get and orders in which to get them are largely suggestions (though you may have trouble getting EP if you get less than suggested). If you're getting one color right after getting another, you should get orange (which you unlock later) first and purple first except for orange, but apart from that it's mostly up to you. Anyway, after getting some purple, you should quickly be able to get <span id="e754"></span> EP, at which point you can do EC8x4, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (<span id="e755"></span>). Now you will have all eternity challenges done, which gives you autobuyers for the things you'd otherwise buy every eternity with EP. You should be able to get here from unlocking chroma in <span id="e756"></span>.</p>
    <p>When you have <span id="e757"></span> EP, you should do another long eternity to get <span id="e758"></span> grey, which takes roughly <span id="e759"></span>. Even though you have more grey than purple at this point, grey is more useful and thus more worth producing.</p>
    <p>You should soon be able to get <span id="e760"></span> EP to unlock orange. Unlock orange, start producing orange, and do an eternity long enough to let you get <span id="e761"></span> orange (which should take roughly <span id="e762"></span>). Then get <span id="e763"></span> purple (which should also take roughly <span id="e764"></span>). Then keep gaining EP. From here on eternities should be roughly as long as it takes to make Study 11 cap, which is currently roughly <span id="e765"></span> but will decrease with additional EP and thus additional eternity stars. You can in fact set your eternity autobuyer to time and get more EP automatically, due to your eternity generator autobuyers and other similar autobuyers. When you get <span id="e766"></span> EP, you should get <span id="e767"></span> grey (which should take <span id="e768"></span>). Then keep gaining EP until <span id="e769"></span> EP, at which point you should do another longer eternity to get <span id="e770"></span> grey (which will take roughly <span id="e771"></span>).</p>
    <p>It will be somewhat hard to get <span id="e772"></span> EP to unlock cyan (permanence upgrade costs will probably be <span id="e773"></span>). Roughly when you unlock cyan, you should get enough theorems to buy Study 3, so do that. You should be able to get here from completing all eternity challenges in <span id="e774"></span>.</p>
    <p>When you unlock cyan, first get <span id="e775"></span> cyan, which should take roughly <span id="e776"></span>. Then keep getting EP. Once you get <span id="e777"></span> EP, get <span id="e778"></span> orange (which takes roughly <span id="e779"></span>) and then <span id="e780"></span> cyan (which takes roughly another <span id="e781"></span>). Then keep getting more EP. When you get <span id="e782"></span> EP, then get <span id="e783"></span> grey (<span id="e784"></span>). Then keep gaining EP. When you get <span id="e785"></span> EP, get <span id="e786"></span> orange (<span id="e787"></span>), then <span id="e788"></span> purple, and then <span id="e789"></span> cyan (both also <span id="e790"></span> each). At <span id="e791"></span> EP, get <span id="e792"></span> grey, which should take roughly <span id="e793"></span>. When you get <span id="e794"></span> EP, get <span id="e795"></span> of orange, purple, cyan, and grey in that order, each taking roughly <span id="e796"></span>.</p>
    <p>When you get <span id="e797"></span> EP, unlock green and start producing it. Buy Study 4 and Study 7 as they become affordable. After you buy them, you'll be able to buy fourth-row studies. For now, buy only Study 16. Once you've bought Study 16 at least once, create a study preset at the bottom of the Studies tab and call it "Chroma". You'll always want to use this preset for gaining chroma. Once the next theorem from green is within <span id="e798"></span> of the chroma cap, or is over the chroma cap, stop producing green. Then create a preset and edit its studies to 1,2,3,4,5,6,7,8,9,10,11,12&s9,10,9,0. This preset will buy roughly the same amount of Studies 13, 14, and 15, except it will be slightly more willing to buy Study 14. Call this preset "Push". You'll always want to use this preset when you're trying to gain EP rather than chroma (well, as long as you have at least <span id="e799"></span> theorems, which you do).</p>
    <p>At <span id="e800"></span> EP, get <span id="e801"></span> of each color, in the order orange, purple, green, cyan, grey (<span id="e802"></span> for each). Remember to use the Chroma preset and turn your eternity autobuyer off. Then use Push to gain more EP. At <span id="e803"></span> EP, gain <span id="e804"></span> of each color, again in the order orange, purple, green, cyan, grey (<span id="e805"></span> to <span id="e806"></span> each). At <span id="e807"></span> EP, produce <span id="e808"></span> of each color (<span id="e809"></span> to <span id="e810"></span> for each). At <span id="e811"></span>, get <span id="e812"></span> of each color (<span id="e813"></span> each). You should soon be able to complexity for <span id="e814"></span> complexity points. Do so as soon as you can. You should be able to get to this point from unlocking cyan in roughly <span id="e815"></span>, or from unlocking chroma in roughly <span id="e816"></span>.</p>
    <p>Studies to use in (and just before) this phase (pre-green):</p>
    <table style="margin-left: auto; margin-right: auto;" style="width: 90%">
      <colgroup>
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 30%;">
         <col span="1" style="width: 30%;">
      </colgroup>
      <tr>
        <td style="text-align: center;">Total EP (roughly)</td>
        <td style="text-align: center;">Total theorems</td>
        <td style="text-align: center;">Eternity Challenge</td>
        <td style="text-align: center;">Studies</td>
        <td style="text-align: center;">Notes</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e817"></span></td>
        <td style="text-align: center;"><span id="e818"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e819"></span></td>
        <td style="text-align: center;"><span id="e820"></span></td>
        <td style="text-align: center;">EC8x2</td>
        <td style="text-align: center;">unlock 9, 10, 11, 12<br/>complete 1, 2, 3, 4, 5, 6, 7, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e821"></span></td>
        <td style="text-align: center;"><span id="e822"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 3, 5, 6, 8, 9, 10, 12</td>
        <td style="text-align: center;">Use this after getting <span id="e823"></span> grey</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e824"></span></td>
        <td style="text-align: center;"><span id="e825"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 5, 6, 8, 9, 10, 11, 12</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e826"></span></td>
        <td style="text-align: center;"><span id="e827"></span></td>
        <td style="text-align: center;">EC8x3</td>
        <td style="text-align: center;">unlock 9, 10, 11, 12<br/>complete 1, 2, 3, 4, 5, 6, 7, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e828"></span></td>
        <td style="text-align: center;"><span id="e829"></span></td>
        <td style="text-align: center;">EC6x4</td>
        <td style="text-align: center;">unlock and complete whatever</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e830"></span></td>
        <td style="text-align: center;"><span id="e831"></span></td>
        <td style="text-align: center;">EC8x4</td>
        <td style="text-align: center;">unlock 9, 10, 11, 12<br/>complete 1, 2, 3, 4, 5, 6, 7, 8</td>
        <td/>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e832"></span></td>
        <td style="text-align: center;"><span id="e833"></span></td>
        <td/>
        <td style="text-align: center;">1, 2, 3, 5, 6, 8, 9, 10, 11, 12</td>
        <td style="text-align: center;">At this point you should have <span id="e834"></span> extra theorems from boost power</td>
      </tr>
    </table>
  </div>
  <div id="b28">
    <h3>Complexity to completing all complexity achievements</h3>
    <p>So, you've complexitied. As with eternity, this resets basically everything. You keep your slow autobuyers, and that's basically it. However, you do have <span id="e835"></span> complexity points (ℂP) and <span id="e836"></span> Complexity Challenge 1 (ℂC1) completion. Complexity challenges will become more relevant and thus more discussed later. For now you can ignore them.</p>
    <p>With your <span id="e837"></span> ℂP, you can, and should, buy a Complexity Generator 1. Complexity generators (ℂGs) are like previous generators except that they cost complexity points. Complexity stars have a single effect, which makes complexity challenge rewards stronger. Note that you start with <span id="e838"></span> complexity stars at the start of each complexity. Note also that before you eternity you have <span id="e839"></span> eternity stars, but they don't do anything until you eternity. Complexity generators reset on complexity as eternity generators do on eternity.</p>
    <p>Multiplier to complexity challenge rewards from complexity stars: (log<span id="e840"></span>(complexity stars)^<span id="e841"></span>)x.</p>
    <p>You won't want to get more than <span id="e842"></span> ℂP per complexity for a while, but just for reference, here's the ℂP formula.</p>
    <p>ℂP formula: (total EP this complexity)^<span id="e843"></span></p>
    <p>In addition to affected complexity generator multipliers, complexities do two other things. They let you automatically complete an EC tier every <span id="e844"></span> / min(<span id="e845"></span>, complexities) seconds, and they multiply chroma buildup speed and permanence gain by <span id="e846"></span>^(min(<span id="e847"></span>, complexities)^<span id="e848"></span>) (this also decreases the required eternities to gain permanence).</p>
    <p>Note that the automatically completed EC tier will be a tier of the first EC you do not yet have <span id="e849"></span> completions of, regardless of which ECs you can unlock, which EC is currently unlocked, or which EC if any you are currently in.</p>
    <p>The second complexity is so much quicker than the first that it feels qualitatively different in many areas, but much of the pre-complexity guide still applies. You should assume the pre-complexity guide applies unless an alternative is presented, or more accurately and generally, assume that you should do whatever you should have done in the previous complexity. So if something is mentioned to have changed in third complexity and nowhere else, you should do it in the old pre-complexity way for the first and second complexities and in the new way for all others.</p>
    <p>The first infinity is much like the first infinity of the second eternity, except even faster, especially after you prestige. After you infinity, buy things in the same order as before, but do <span id="e850"></span> infinities before doing any challenges. At this point all the challenges should be very easy. Some of the challenges are hard in the sense that they might take <span id="e851"></span>; Normal Challenge 2 and Normal Challenge 7 are hard only because they still require autobuyers to be off, Normal Challenge 3 is hard due to remaining slow initially, and Normal Challenge 10 is hard because it still requires a lot of sacrificing.</p>
    <p>When you complete all the challenges, break infinity. Set the sacrifice autobuyer to <span id="e852"></span>x and set the prestige autobuyer to <span id="e853"></span>. With infinities roughly <span id="e854"></span> long, you should reach IC1 in less than <span id="e855"></span>. Before starting IC1, do infinities for <span id="e856"></span> IP until you get <span id="e857"></span> infinities. IC1 still requires you to turn autobuyers off, but you don't need to wait to prestige at all. You should be able to unlock IC2 in roughly <span id="e858"></span>; do it when you can unlock it. It should be fairly easy. Don't do IC3 or IC5 as soon as you can unlock them. When you can unlock IC5, do IC3 and IC5. For IC3, turn the prestige autobuyer off and don't worry that much about when you prestige, since IC3 is easy now. For IC5, set the prestige autobuyer to <span id="e859"></span> (on, of course). Don't do any more ICs until you can eternity, in roughly <span id="e860"></span>. When you can eternity, don't do so immediately. Instead, do IC6 (following the above strategy, but it should be quicker; you may need to turn the boost autobuyer off in your first prestige to avoid getting too many stars), and do IC7 (which should be very easy). Buy a theorem with stars and a theorem with IP. When you get <span id="e861"></span> IP, do IC8, but you only need <span id="e862"></span> purchases if you prestige manually a few times after building up purchases rather than using the prestige autobuyer. Now do IC4, with autobuyers set to trigger every <span id="e863"></span> and prestige autobuyer set to <span id="e864"></span>. IC4 should take roughly <span id="e865"></span>. You should now have done all ICs.</p>
    <p>Set prestige autobuyer to <span id="e866"></span> and infinity autobuyer to <span id="e867"></span>x best of last ten. You should be able to get another theorem with stars and another theorem with IP in <span id="e868"></span> or less, giving you <span id="e869"></span> total theorems. Buy Study 3. When you can get <span id="e870"></span> EP, do so, and buy EG1 and a theorem with EP. It should take roughly <span id="e871"></span> from complexity to get here.</p>
    <p>Now that you have Study 3, eternities are very fast. First infinity and all the challenges, even Normal Challenge 7, can be completed by maxing all a few times. IC1 is both easy and the only IC worth doing. Keep your infinity autobuyer at <span id="e872"></span>x best of last ten. Do eternities for <span id="e873"></span> EP until you have <span id="e874"></span> eternities. When you get <span id="e875"></span> eternities, you no longer have to do IC1 yourself. When you get <span id="e876"></span> eternities, make the sacrifice autobuyer <span id="e877"></span>x. When you get <span id="e878"></span> eternities, make the prestige autobuyer <span id="e879"></span>x and the infinity autobuyer <span id="e880"></span>. You should mostly save up for EG2 in this phase. These eternities will decrease in length from <span id="e881"></span> to <span id="e882"></span>.</p>
    <p>After you get <span id="e883"></span> eternities, set the infinity autobuyer to <span id="e884"></span> since total, turn the eternity autobuyer off, and do a longer eternity. Even if you can't buy any theorems with EP, you should easily be able to get <span id="e885"></span> theorems. When you do, buy Study 2. Eternity when it will increase your current EP to <span id="e886"></span>, which is enough to buy <span id="e887"></span> total theorems with EP (<span id="e888"></span> which is already boughts, <span id="e889"></span>, <span id="e890"></span>, <span id="e891"></span>) and you have at least <span id="e892"></span> theorems not bought with EP. This should take roughly <span id="e893"></span>. Then do another longer eternity like the previous, with Study 1 in addition to Studies 2 and 3 this time. You should be able to get <span id="e894"></span> total theorems and over <span id="e895"></span> EP on eternity, at which point you should eternity, get another theorem with EP, and buy Study 4.</p>
    <p>At this point, set your infinity autobuyer to <span id="e896"></span> and your eternity autobuyer to <span id="e897"></span> EP. Each eternity will take roughly <span id="e898"></span>. At roughly <span id="e899"></span> eternities they'll take only <span id="e900"></span>; then change the infinity autobuyer to <span id="e901"></span> IP. When you get <span id="e902"></span> eternities, do another longer eternity like those before. Eternity when you can get <span id="e903"></span> EP, which should take roughly <span id="e904"></span>. Buy EG3. Now do another longer eternity. Set your infinity autobuyer to <span id="e905"></span> after <span id="e906"></span>. Eternity when you can gain at least <span id="e907"></span> EP and have at least <span id="e908"></span> boost power, which should take roughly <span id="e909"></span>. Buy the second eternity upgrade with the EP you get. Now do an eternity to gain <span id="e910"></span> EP (<span id="e911"></span>), and spend them on a theorem. You should now have <span id="e912"></span> theorems.</p>
    <p>Generally from here on, you'll want to aim for getting extra theorems with boost power a lot later than according to the pre-complexity guide, meaning you may have a few fewer theorems than the pre-complexity guide suggests at any given point. Get <span id="e913"></span> eternities rather than <span id="e914"></span>. After you first get <span id="e915"></span> EP, do another eternity to get another theorem with IP and roughly <span id="e916"></span> EP so you can get <span id="e917"></span> theorems.</p>
    <p>Roughly when you unlock the Eternity Producer, you will automatically complete EC1x1, which will give you another theorem. It'll also make progress significantly quicker. However, progress will slow down somewhat; the eternity after which you get EG7 will take roughly <span id="e918"></span> and will give you a theorem for getting <span id="e919"></span> boost power, if you don't have that theorem already. The eternity after which you get EG8 will take roughly <span id="e920"></span> (which is slightly longer than the eternities leading up to EG8). It should take roughly <span id="e921"></span> from eternity to get EG8, or equivalently <span id="e922"></span> from complexity.</p>
    <p>You'll only have <span id="e923"></span> total theorems for EC2x1 so you'll need to do 5, 6, 8, 9 for unlock. After completing EC2x1, you should have <span id="e924"></span> theorems, and should use studies 3, 5, 6, 8, 9 due to 3 being slightly better than 7 (largely because 7 has not reached its cap). At roughly <span id="e925"></span> EP, it is worth doing a longer eternity in which you try to get an extra theorem from <span id="e926"></span> boost power, so that you can get <span id="e927"></span> total theorems. Set your infinity autobuyer to <span id="e928"></span>. Getting this theorem will take roughly <span id="e929"></span>. After you get it, switch to 5, 6, 8, 9, 10 and set your infinity autobuyer back to <span id="e930"></span>.</p>
    <p>At this point, you should almost have another EC tier autocompletion, but it will complete EC1x2 if you do nothing, and you'll be able to complete EC1x2 soon yourself. So, you should turn EC autocompletion off until you complete EC1x2. The EC autocompletion timer will keep counting down, but if it hits <span id="e931"></span> it will just store an EC autocompletion that will be used when you turn EC autocompletion back on. You should do both EC1x2 (complete 8, 9, 10, 12) and EC4x1 at <span id="e932"></span> total EP, one right after the other. After EC1x2 but before EC4x1, you should turn autocomplete back on and thus automatically complete EC1x3. You should wait to do EC3x1 until <span id="e933"></span> EP, wait to do EC1x4 and EC3x2 until <span id="e934"></span> EP, wait to do EC3x3 until <span id="e935"></span> EP, wait to do EC2x3 until <span id="e936"></span> EP, and wait to do EC3x4 until <span id="e937"></span> EP.</p>
    <p>After doing EC2x4, you'll be close to getting another autocompletion, which will be of EC4x3 if you don't do anything. It's worth putting this autocompletion off a bit so it's of EC4x4, by turning autocompletion off. If you can't afford Study 10 for EC6x1, use Study 2 instead (so 2, 3, 5, 6, 8, 9). You should now have <span id="e938"></span> EC completions. It takes <span id="e939"></span> from EG8 to get here, or <span id="e940"></span> from complexity.</p>
    <p>At this point you should be gaining boost power quickly enough that it's worth getting another theorem from <span id="e941"></span> boost power (<span id="e942"></span> to <span id="e943"></span>). Generally you should from now on use the EP requirements given in the guide for EC tiers, not the permanence upgrade requirements. After doing EC4x3, turn autocompletion back on; it will autocomplete EC4x4. Wait to do EC6x2 until <span id="e944"></span> EP and <span id="e945"></span> permanence upgrade costs, and use 3 instead of 11 for EC6x2 (so use 3, 5, 6, 8, 9, 10, 12). You'll soon have the option of Study 2 or Study 11; since progress is faster, you almost always want to pick Study 2, even when the pre-complexity guide suggests Study 11. Use 3 instead of 11 for EC7x2 (so use 3, 5, 6, 8, 9, 10, 12). After EC7x2, due to EC4x4 autocompletion you'll have <span id="e946"></span> EC tiers completed.</p>
    <p>Do EC7x3 as soon as you can unlock it (<span id="e947"></span> EP) and wait to do 6x3 (which can also be done with 3, 5, 7, 8, 9, 10, 12 at this point) until you've done EC7x3. Soon you'll get another EC tier autocompletion; if you don't do anything it will give EC6x4, which is a very good EC tier to have, so let it happen. When you get <span id="e948"></span> theorems, use studies 1, 2, 3, 5, 6, 8, 9, 10, 12 and keep them even when you could swap 3 for 11; your eternities won't generally be long enough that you'd want to do that. You'll automatically complete EC6x4 after completing EC8x2, and EC6x4 should allow you to easily unlock chroma. It takes <span id="e949"></span> from <span id="e950"></span> EC completions to get here, or <span id="e951"></span> from complexity.</p>
    <p>You'll generally need to get chroma later (in terms of EP) now than pre-complexity, and it will be roughly <span id="e952"></span>x faster. You can get to <span id="e953"></span> EP with a very small amount of grey, and even somewhat beyond it, but at roughly that point you should do a longer eternity to get <span id="e954"></span> grey (roughly <span id="e955"></span>). At <span id="e956"></span> EP, do a longer eternity to get <span id="e957"></span> grey (<span id="e958"></span>). You can do EC8x4 long before it is autocompleted. After doing EC8x4, get <span id="e959"></span> purple (<span id="e960"></span>). Typical eternities at this point should be roughly <span id="e961"></span> long. At <span id="e962"></span> EP, you should get <span id="e963"></span> grey (<span id="e964"></span>). When you get <span id="e965"></span> total theorems, buy Study 4, making your studies 1, 2, 3, 4, 5, 6, 8, 9, 10, 12. When you unlock orange, get <span id="e966"></span> orange, then <span id="e967"></span> purple, and then <span id="e968"></span> grey (<span id="e969"></span> each). At <span id="e970"></span> EP, get <span id="e971"></span> grey, as you did pre-complexity (<span id="e972"></span> to <span id="e973"></span>). When you get <span id="e974"></span> total theorems, swap Study 4 for Study 11, making your studies 1, 2, 3, 5, 6, 8, 9, 10, 11, 12. Study 11 is still fairly weak but it's better than Study 4.</p>
    <p>When you unlock cyan, first get <span id="e975"></span> cyan, which should take roughly <span id="e976"></span>. Then keep getting EP. At first you should do eternities that are <span id="e977"></span> long, going up to <span id="e978"></span> when after only <span id="e979"></span> you get less than <span id="e980"></span>x EP per eternity. At <span id="e981"></span> EP, get <span id="e982"></span> of each color in the order orange, purple, cyan, grey (<span id="e983"></span> to <span id="e984"></span> each). At <span id="e985"></span> EP, get <span id="e986"></span> of orange, purple, cyan, grey (<span id="e987"></span> to <span id="e988"></span> each). When you unlock green, start producing green as you did pre-complexity, using the Chroma preset. Getting chroma of each color is now so quick that you should do it whenever you can't get <span id="e989"></span>x EP in <span id="e990"></span>. Eventually you should be able to complexity again for <span id="e991"></span> ℂP, with far less trouble than the first time. You can get here in <span id="e992"></span> from unlocking chroma, or <span id="e993"></span> from complexity.</p>
    <p>At this point, you can either complexity, or get ℂC1x2, which requires <span id="e994"></span> stars. Though the guide was written from a perspective of ℂC1x2 not being optimal, ℂC1x2 seems optimal now (due either to game changes since the guide was written or to that perspective just having been wrong). If you've been playing very actively and gotten here in something close to the time suggested by the guide, this may be somewhat hard (take <span id="e995"></span>). However, if this complexity has taken more like <span id="e996"></span>, then, due to having more complexity stars, it may take less than <span id="e997"></span> to get to ℂC1x2, which is then clearly worthwhile.</p>
    <p>Note that whatever you do, it's very important to disable buying of boosts, either just before or just after you complexity, so that you're in ℂC2. This is described more below, but it's important enough that it deserves its own paragraph so that it's easier to notice.</p>
    <p>If you really don't like waiting, you don't absolutely need to get ℂC1x2. However, otherwise, you should get it. It will allow you to easily get "Forever isn't too long", get more ℂC2 completions, and complexity again (even getting ℂC1x3) in roughly <span id="e998"></span>. An important note is that this section of the guide was written without ℂC1x2 yet and hasn't yet been rewritten (except for a few small parts), so if you want to follow the guide exactly, you might not want to get ℂC1x2 yet. If you scroll down to the fourth complexity description (starting with "You should be able to figure out how to do a complexity now"), it's much like the third complexity with ℂC1x2 is. I'm sorry.</p>
    <p>In any case, after getting ℂC1x2, there's nothing else worth trying to get, so complexity.</p>
    <p>Now you have <span id="e999"></span> complexities and can start doing complexity challenges. Complexity challenges are very different from the previous types of challenges. They have star requirements and do not require you to infinity, eternity, or complexity for completion. They can be completed any number of times (though they get harder each time), like eternity challenges without the limit of <span id="e1000"></span> completions each. Most importantly, however, each complexity challenge has a condition rather than being entered explicitly. For as long in a complexity as you observe the condition, you stay in the complexity challenge, and once you break the condition you exit the complexity challenge. Now that you have <span id="e1001"></span> complexities, you should get some completions of ℂC2, which has the condition that you can't buy boosts. In the Complexity Challenges tab you can disable buying of boosts, and you should do this.</p>
    <p>You get complexity achievements for getting certain amounts of progression in complexity challenges. Complexity achievements have various types of rewards of varying significance. Right now you'll want the first two complexity achievements, "One per generator" and "Forever isn't too long". (Without ℂC1x2, which is what this section of the guide was originally written for, "Forever isn't too long" will take roughly <span id="e1002"></span> due to EC1 autocompletions, so may not be worth getting and was thus not originally recommended. Specifically, without ℂC1x2, <span id="e1003"></span> EC1 autocompletions are required for "Forever isn't too long"; this will let you get Study 3 and make "Forever isn't too long" easy.)</p>
    <p>The early part of the third complexity will be somewhat slower than that of the second due to you not buying boosts. However, the strategy is generally similar before breaking infinity. You can now do Normal Challenge 9 immediately without losing anything since you're not buying boosts anyway. It helps that boosts are helpful later in an infinity and the later part of an infinity is already fast. Otherwise, behaving as for your last complexity until you break infinity works. When you break infinity, you'll notice that progression slows down. You'll want to set the prestige autobuyer to <span id="e1004"></span>x rather than <span id="e1005"></span> second. This likely goes without saying but the first infinity upgrade is basically useless at this point. You should get <span id="e1006"></span> IP (and <span id="e1007"></span> ℂC2 completion) roughly <span id="e1008"></span> after complexity. At this point, get <span id="e1009"></span> infinities, and then keep getting more IP. From here on, progression will feel much like it was between <span id="e1010"></span> and IC1 in first eternity, except somewhat faster. Roughly when you unlock IC1, you'll autocomplete EC1x1, which will make it far easier to unlock IC1 if you haven't done that yet and to complete IC1. You should get <span id="e1011"></span> completions of ℂC2, and with them "One per generator", roughly <span id="e1012"></span> after your first ℂC2 completion or <span id="e1013"></span> after complexity.</p>
    <p>Getting to eternity is fairly straightforward; you can skip IC4 and IC8, but not IC6. IC7 does nothing except a small boost to infinity generators, which you can ignore, so you don't need it.</p>
    <p>After getting to eternity, since you then get "Forever isn't too long", you can exit ℂC2 by re-enabling buying of boosts in the Complexity Challenges tab. You'll have <span id="e1014"></span> ℂC2 completions. If for some reason, such as stepping away for a few minutes, you got a lot more stars and IP after becoming able to eternity but before exiting ℂC2, you may have <span id="e1015"></span> completions instead, or more. These few extra completions may slightly speed up this complexity overall. So if you want, you can try to get them, perhaps by doing a few more eternities to be able to afford Study 3. However, they're not necessary; their effect is fairly minimal at this point.</p>
    <p>From here on the third complexity is much like the second, except faster. Set your prestige autobuyer back to <span id="e1016"></span>. You can skip IC4. You have <span id="e1017"></span> "extra" theorem from EC1x1, which helps in getting studies slightly. After <span id="e1018"></span> eternities, you should be able to progress far faster than in second complexity. Your eternities should generally be between <span id="e1019"></span> and <span id="e1020"></span>, and they should each give significantly more EP than the last (except when you do quick eternities to get <span id="e1021"></span> eternities, which you should do at roughly <span id="e1022"></span> total EP). There's no need to get more than <span id="e1023"></span> eternities before the Eternity Producer. You'll generally want your infinity autobuyer at <span id="e1024"></span> seconds rather than <span id="e1025"></span> due to how quick progress is. The eternity in which you get EG7 is somewhat long, being roughly <span id="e1026"></span>. When you get EG7, you should be close to getting your second EC autocompletion; it's fine to keep autocomplete on and get EC1x2. You can get EG8 roughly <span id="e1027"></span> after exiting ℂC2, or <span id="e1028"></span> after complexity.</p>
    <p>You may not have the theorem for <span id="e1029"></span> boost power yet. If you don't, do an eternity that's as long as needed for you to get it (probably roughly <span id="e1030"></span>). At <span id="e1031"></span> EP, change your infinity autobuyer to <span id="e1032"></span> seconds. Do EC4x1 at <span id="e1033"></span> EP as you did second complexity, but you should wait to do EC3x1 until <span id="e1034"></span> EP, EC1x3 until <span id="e1035"></span> EP, and EC1x4 and EC3x2 until <span id="e1036"></span> EP. Complete EC3x1 with 3, 7, 8, 9, 12, since you can afford Study 7 now.</p>
    <p>You will soon get a third EC autocompletion. You're close to doing EC2x2 yourself and progress is fast, so you should turn autocompletion off. Do EC2x2 at <span id="e1037"></span> EP, EC3x3 at <span id="e1038"></span> EP, and EC2x3 at <span id="e1039"></span> EP. After doing EC4x3, you can turn autocomplete back on and autocomplete EC4x4. Due to how quickly you're going, you may get less permanence with the same EP, making third-row studies worse compared to first-row studies; you should use studies 1, 2, 3, 5, 6, 8, 9, 10 when you can afford them. After completing EC5x3, you should have a fourth EC autocompletion coming soon; turn EC autocompletion off so you can use it when it's more helpful. Do EC6x2 at <span id="e1040"></span> EP, and switch to 1, 2, 5, 6, 8, 9, 10, 12 after completing EC6x2. After doing EC6x3, you can turn autocomplete back on and autocomplete EC6x4. You can unlock chroma roughly <span id="e1041"></span> after getting EG8, or <span id="e1042"></span> after complexity.</p>
    <p>At this point you should be able to figure out roughly when to get chroma. You'll probably want to do it somewhat less than you did second complexity. You can reach the point where you can complexity roughly <span id="e1043"></span> after unlocking chroma, or <span id="e1044"></span> after complexity.</p>
    <p>However, rather than complexitying at that point, you should try to get ℂC1x2 (if you didn't before). This requires <span id="e1045"></span> stars, or <span id="e1046"></span> EP. You should get ℂC1x2 roughly <span id="e1047"></span> after being able to complexity, or <span id="e1048"></span> after complexity. (Commentary: Aren't you glad you got ℂC1x2 and this only took <span id="e1049"></span>? Also, you can get ℂC1x3 now, included in the given time estimate.) At this point, complexity for <span id="e1050"></span> ℂP again.</p>
    <p>You should be able to figure out how to do a complexity now, especially since ℂC1x2 will make it a lot easier. Buy another ℂG1 for 4 ℂP. Enter ℂC2 again as before. From IC1 on, ℂC2 will be much like first complexity but somewhat quicker. Between unlocking IC4 and unlocking IC5 you should get EC1x1, which should help. Skip IC4, IC7, and IC8. After you eternity, you will get "Forever isn't too long". This will make it so you have <span id="e1051"></span> more eternities, for a total of <span id="e1052"></span>. This will make it easy to get <span id="e1053"></span> eternities while still in ℂC2. You should be able to get <span id="e1054"></span> theorems and then <span id="e1055"></span> ℂC2 completions without much trouble. Once you get <span id="e1056"></span> ℂC2 completions, exit ℂC2. (Note: You may have already got this many in your third complexity, in which case it isn't worth getting them now. In fact, getting "Forever isn't too long" in your third complexity necessarily gives you enough ℂC2 completions that it's not clearly worth getting more now.)</p>
    <p>You will get <span id="e1057"></span> EC autocompletions before you complete all EC tiers. The game is now fast enough that it doesn't matter that much if or when you use them. Towards the end of this complexity, you might notice that you can get chroma even when you use the "Push" preset, and thus switching between Chroma and Push can be replaced by just using Push all the time. You should complexity once you get ℂC1x3. This requires <span id="e1058"></span> stars, or <span id="e1059"></span> EP. However, read the following paragraph first. This complexity should take roughly <span id="e1060"></span>.</p>
    <p>You now have <span id="e1061"></span> complexities. This will let you do ℂC3. ℂC1x3 will also let you do a few more tiers of ℂC2. (Later comment: This is true but I'm not sure it's worth the extra time.) So disable buying boosts (do this before you complexity, since otherwise you'll buy boosts before you can disable them) and disable unlocking the Eternity Producer. Technically you could leave unlocking the Eternity Producer enabled and you would remain in ℂC3 until you actually unlock it, but it is good to remove the risk of accidentally unlocking it.</p>
    <p>You start with <span id="e1062"></span> eternities, so there's no need to do eternities to get automation. Once you get <span id="e1063"></span> ℂC2 completions, exit ℂC2, that is, re-enable buying boosts. Unlocking the Eternity Producer should remain disabled, though. Note that once you have <span id="e1064"></span> EC completions, you will still get a multiplier to eternity gain, but it won't help you get permanence because gaining permanence requires the Eternity Producer to be unlocked. You'll get an EC autocompletion; EC4x4 is a good choice to use it on (since otherwise you won't complete EC4x4 in ℂC3 at all) but you don't need to use it at all, and if you do use it it's not too important where. You should get "Actually a boost" naturally, at roughly <span id="e1065"></span> EP.</p>
    <p>After roughly <span id="e1066"></span> in complexity, you can reach <span id="e1067"></span> EP, ℂC3x9, and ECs 4/4/4/3/3/1/1/0 (EC1x4, EC2x4, ..., EC7x1, no EC8). At this point, do eternities as quickly as possible (infinity for <span id="e1068"></span> IP, eternity whenever possible). After roughly <span id="e1069"></span>, you will get "Time after time". The default setting of the permanence autobuyer (<span id="e1070"></span> times last) is good. Exit ℂC3 by re-enabling unlocking the Eternity Producer and then actually unlocking the Eternity Producer. Complexity when you can gain <span id="e1071"></span> ℂP, at <span id="e1072"></span> EP. You will still only have ℂC1x3 (not ℂC1x4). This should take roughly <span id="e1073"></span>.</p>
    <p>You now have <span id="e1074"></span> complexities. This complexity should be fairly straightforward. You shouldn't try to get any complexity challenge completions. EC1 and EC3 are at this point far harder than the other ECs compared to their original difficulty (so EC3 is still easier than EC2 and EC4 in general, and EC1 is still the easiest, just not by as much). You'll get <span id="e1075"></span> EC autocompletion and it doesn't matter much where you use it. Complexity when you can gain <span id="e1076"></span> ℂP; this may feel harder than it did last complexity because you have fewer complexity stars due to getting to the end of your complexity more quickly. This complexity should take roughly <span id="e1077"></span>.</p>
    <p>You now have <span id="e1078"></span> complexities and <span id="e1079"></span> complexity points. Save for ℂG2 rather than buying ℂG1 again. Also, enter ℂC4. Also, turn EC autocomplete off if it's on, since you'll be trying to get "Broke every stone" this complexity. Even though you don't have chroma, you should be able to do EC8x3, EC6x4, and EC8x4 as soon as you can unlock them. This will give you "Broke every stone", which will be very convenient for doing ECs in the future. At <span id="e1080"></span> EP, you should be able to easily get "No rest" by entering EC2 after roughly <span id="e1081"></span>. After this point, do eternities which are <span id="e1082"></span> long. <span id="e1083"></span> later, or equivalently <span id="e1084"></span> after complexity, you should get ℂC4x7. At this point, exit ℂC4. (People have pushed forward and gotten Shadeless in this complexity, but it takes a while and though Shadeless is wonderful quality of life, I can't recommend it unless you're fairly idle.) Don't try for ℂC1x4, since it's still somewhat too hard. Complexity when you can gain <span id="e1085"></span> ℂP. This complexity should take roughly <span id="e1086"></span>.</p>
    <p>You now have <span id="e1087"></span> complexities and <span id="e1088"></span> complexity points. This complexity should be fairly straightforward. At this point you can change the initial part of the Push preset (before &amp;) to 5,6,8,9,10,12,1,2,3,11,4,7. From now on (including in later complexities) this version of the Push preset should be enough to get you through the early part of a complexity, except in some hard complexity challenges such as the upcoming ℂC6. However, using it in some ECs will make them harder. You can either load the preset and respec whenever you can buy a new study, or load only when you can buy the next study in the list; if you constantly load the preset without respeccing, you may buy a later study (for example, Study 7) while unable to afford an earlier one, which is a short-term boost but will be bad eventually if you don't respec.</p>
    <p>You shouldn't try to get any complexity challenge completions. You should consider "Broke every stone" mostly as not forcing you to unlock ECs and letting you do some later ECs slightly early; you still can't generally do ECs much earlier or complete an EC multiple times at once (sometimes you can complete the last <span id="e1089"></span> tiers of an EC together, though). This complexity should take roughly <span id="e1090"></span>.</p>
    <p>You now have <span id="e1091"></span> complexities and <span id="e1092"></span> complexity points. Do ℂC5. Note that by this point in the game, manual infinities might be faster than using the infinity autobuyer due to being easier to adjust. You should be able to get ℂC5x2 in roughly <span id="e1093"></span>, at which point you should exit ℂC5. After only roughly <span id="e1094"></span> more you should get ℂC1x4, and you should then complexity. This complexity should take roughly <span id="e1095"></span>.</p>
    <p>You now have <span id="e1096"></span> complexities and <span id="e1097"></span> complexity points. Spend <span id="e1098"></span> ℂP on ℂG2. You can now easily get more completions of several complexity challenges. This complexity, do ℂC4. You could also do ℂC3 at this point, but "Shadeless" is such wonderful quality of life and raising the chroma cap is so valuable that ℂC4 is good to do first. Once you complete all ECs, due to not being able to get chroma you can mostly just do eternities that are <span id="e1099"></span> to <span id="e1100"></span> long (<span id="e1101"></span> initially, then <span id="e1102"></span> when progress gets slow). You should get ℂC4x13 in <span id="e1103"></span>, giving you "Shadeless", and ℂC4x14 less than <span id="e1104"></span> later. Exit ℂC4. You should then get 3 ℂP less than <span id="e1105"></span> after exiting ℂC4. This complexity should take roughly <span id="e1106"></span>.</p>
    <p>You now have <span id="e1107"></span> complexities and <span id="e1108"></span> complexity points. Do ℂC3. Get <span id="e1109"></span> eternities early (once eternities take less than <span id="e1110"></span>). In the last few complexities you've been able to rely on the Eternity Producer, but you can't do that here. After roughly <span id="e1111"></span> EP, because you can't get permanence upgrades (permanence requires the Eternity Producer), third-row studies are useless to an extent comparable to how useless Study 7 is (most are slightly better than Study 7, though Study 11 is slightly worse). You should be able to unlock chroma, giving you "After a hurricane" and <span id="e1112"></span> complexity achievements, in roughly <span id="e1113"></span>. After <span id="e1114"></span> EP, you should be able to do eternities that are <span id="e1115"></span> long. (Just after <span id="e1116"></span> EP you might want to intermittently do eternities that are <span id="e1117"></span> seconds long for chroma, but by <span id="e1118"></span> EP, <span id="e1119"></span> should be enough for chroma.) You can get very far in ℂC3, but progress will slow down slightly just before ℂC3x36, roughly when you get "3 * 7 * 11". Do eternities that are <span id="e1120"></span> long at this point until you get ℂC3x36. When you get ℂC3x36, exit ℂC3 and complexity (or complexity and then exit). This complexity should take roughly <span id="e1121"></span>.</p>
    <p>You now have <span id="e1122"></span> complexities and <span id="e1123"></span> complexity points. Don't do any complexity challenges for this complexity. Progress will be very quick. Complexity as soon as you can get 3 ℂP. This complexity should take roughly <span id="e1124"></span>.</p>
    <p>You now have <span id="e1125"></span> complexities and <span id="e1126"></span> complexity points. Spend <span id="e1127"></span> ℂP on ℂG1, since you're not really saving ℂP for anything right now. Disable buying studies (or in other less precise words, enter ℂC6). Turn EC autocompletion off if you have it on, since you'll be trying to get "Calm EC". Note that you'll get enough eternities to gain permanence even before completing <span id="e1128"></span> EC tiers, and if you leave the game for a few hours you may have more permanence than expected, which may let you do certain EC tiers earlier than you otherwise could. The third permanence upgrade is useless while you're in ℂC6 since you can't buy studies, so so you can turn its autobuyer off if you want, but doing so is not that helpful and the benefits are perhaps outweighed by the fact that you might forget to turn the autobuyer back on.</p>
    <p>The following sentence gives the order you should do EC tiers in and how much EP you should do them at. Do EC2x1 at <span id="e1129"></span> EP, EC4x1 at <span id="e1130"></span> EP, EC1x1 at <span id="e1131"></span> EP, EC3x1 at <span id="e1132"></span> EP, EC1x2 at <span id="e1133"></span> EP, EC2x2 at <span id="e1134"></span> EP, EC1x3 at <span id="e1135"></span> EP, EC3x2 at <span id="e1136"></span> EP, EC1x4 at <span id="e1137"></span> EP, EC3x3 at <span id="e1138"></span> EP, EC2x3 at <span id="e1139"></span> EP, EC4x2 at <span id="e1140"></span> EP, EC3x4 at <span id="e1141"></span> EP, EC2x4 at <span id="e1142"></span> EP, EC5x1 at <span id="e1143"></span> EP, EC6x1 at <span id="e1144"></span> EP, EC4x3 at <span id="e1145"></span> EP, EC5x2 at <span id="e1146"></span> EP, EC5x3 at <span id="e1147"></span> EP, and EC7x1 at <span id="e1148"></span> EP. Doing EC6x1 and thus getting <span id="e1149"></span> EC tiers should take roughly <span id="e1150"></span>, and doing EC7x1 and thus getting <span id="e1151"></span> EC tiers and "Calm EC" should take roughly <span id="e1152"></span> more, or equivalently <span id="e1153"></span> total.</p>
    <p>After getting "Calm EC", you will have all ECs complete. This will allow you to get ℂC6x12 almost immediately. Do a long eternity to accumulate boost power and thus get "Power beats knowledge". This eternity will be roughly <span id="e1154"></span> long. Once you get "Power beats knowledge", you should be able to get ℂC6x13 almost immediately. Once you get ℂC6x13, exit ℂC6 and buy studies again. In this complexity you should try to get <span id="e1155"></span> ℂP and ℂC1x5, both of which require almost exactly the same amount of progress. To do this, your eternities may need to be <span id="e1156"></span> long right before <span id="e1157"></span> ℂP. After getting <span id="e1158"></span> ℂP and ℂC1x5 but before you complexity, disable buying boosts. This complexity should take roughly <span id="e1159"></span>.</p>
    <p>You now have <span id="e1160"></span> complexities and <span id="e1161"></span> complexity points. You'll be getting a lot of ℂC2 completions. Remember to unlock the Eternity Producer when possible (which is almost immediately due to "Calm EC"). The good studies are 2, 3, 4, 6, 7, 8, 9, 10, 12. Studies 1 and 5 are useless in ℂC2, and Study 11 is too slow. Thanks to "3 * 7 * 11" uncapping Study 7 and making it stronger, though, Study 7 is decent. Get Cℂ2x60, which you can do in roughly <span id="e1162"></span>, then exit ℂC2. Remember to unlock chroma and colors of chroma as it becomes possible to do so. As you did last complexity, get <span id="e1163"></span> ℂP. The extra ℂC2 completions should make this far easier. Turn off theorem autobuyers right before you complexity, because next complexity you'll be trying to get "Thousand-theorem twilight". This complexity should take <span id="e1164"></span>.</p>
    <p>You now have <span id="e1165"></span> complexities and <span id="e1166"></span> complexity points. Enter ℂC4 (that is, disable unlocking chroma). Note that you can buy studies, and will still get theorems from several sources (boost power, EC completions, ℂC6). You just can't buy theorems. 5, 6, 7, 9, 10 are good studies to use up until <span id="e1167"></span> EP, at which point you should switch to 1, 5, 6, 9, 10 (replacing 7 by 1). At <span id="e1168"></span> EP, switch to 1, 5, 6, 9, 11 (replacing 10 by 11). When you can buy Study 2, do so, making your studies be 1, 2, 5, 6, 9, 11. (You should have this by when you get <span id="e1169"></span> EP, within roughly <span id="e1170"></span>.) Just before you get "Thousand-theorem twilight", your eternities may need to be roughly <span id="e1171"></span> long. Getting "Thousand-theorem twilight" should take roughly <span id="e1172"></span>.</p>
    <p>When you get "Thousand-theorem twilight", you'll have <span id="e1173"></span> complexity achievements. The <span id="e1174"></span> remaining ones are "More colorful than a potato", "Forgot something", "Nonzero-color theorem", and "On the other side". Turn your theorem autobuyers back on. You'll have ℂC4x16. ℂC4x17 is too hard to get to be worth it, so exit ℂC4. At <span id="e1175"></span> EP, which is also where you can get <span id="e1176"></span> ℂP on complexity and ℂC1x5, you can unlock the new color, which is red. Do so. Note that the multiplier softcap is the number shown near the bottom of the main tab above which normal generator multipliers are reduced. It's initially <span id="e1177"></span>, which you reached even before complexity, but red will increase it (which also makes the softcap have less of an effect when it does apply). Red may seem weak now, but it will get much stronger with more red and more eternities.</p>
    <p>You'll be able to get much farther this complexity than before. Set your eternity autobuyer to <span id="e1178"></span>, and increase it to <span id="e1179"></span> at <span id="e1180"></span> ℂP gained on complexity. Wait to complexity until you get ℂC1x8, at which point you should gain <span id="e1181"></span> ℂP. This complexity should take <span id="e1182"></span>.</p>
    <p>You now have <span id="e1183"></span> complexities and <span id="e1184"></span> complexity points. Buy ℂG1 again. Enter ℂC6; in this complexity you'll be trying to get "Nonzero-color theorem" (but not yet "On the other side"). Remember to unlock the Eternity Producer. Initially, eternity every <span id="e1185"></span>, and more often in roughly the first <span id="e1186"></span> when even very short eternities can be good. You should reach <span id="e1187"></span> EP in at most roughly <span id="e1188"></span>. After reaching <span id="e1189"></span> EP, set the eternity autobuyer to <span id="e1190"></span>. At <span id="e1191"></span> EP, set the eternity autobuyer to <span id="e1192"></span>. You should be able to unlock chroma after roughly <span id="e1193"></span>. Unlock chroma but do not yet exit ℂC6. Turn the eternity autobuyer off, get <span id="e1194"></span> grey, then turn the eternity autobuyer back on. You should get ℂC6x18 roughly <span id="e1195"></span> after complexity. When you get ℂC6x18, exit ℂC6.</p>
    <p>Unlocking red should now be easy; it should take at most <span id="e1196"></span> from exiting ℂC6 if you eternity manually. When you unlock red, set the eternity autobuyer to <span id="e1197"></span>. Get ℂC1x11. Before you complexity but after you get ℂC1x11, disable buying boosts in preparation for the next complexity. You will get at least <span id="e1198"></span> ℂP from this complexity, and maybe <span id="e1199"></span> depending on if you eternity after ℂC1x11 and, if you do, how much EP you eternity for. The guide will assume you got <span id="e1200"></span> ℂP, and it is not important. This complexity should take <span id="e1201"></span>.</p>
    <p>You now have <span id="e1202"></span> complexities and <span id="e1203"></span> complexity points. Buy ℂG1 again; you're not really saving up for anything right now. Since you disabled buying boosts, you should now be in ℂC2. Advice is similar to the last time you did ℂC2, except that you should buy Study 11 when you can, and at that point it will be somewhat useful. Set the eternity autobuyer to <span id="e1204"></span>. Once you get <span id="e1205"></span> EP, set the eternity autobuyer to <span id="e1206"></span> instead, for the sake of making Study 11 stronger.</p>
    <p>You should be able to unlock chroma after roughly <span id="e1207"></span>, giving you "More colorful than a potato". However, grey, which is the only color that will be unlocked initially, is useless at this point. You should still stay in ℂC2 to get "Forgot something", though. You should get <span id="e1208"></span> total theorems roughly <span id="e1209"></span> after complexity). Once you get <span id="e1210"></span> total theorems, respec studies and buy every study other than a single third-row study (such as Study 12) to get "Forgot something". Then exit ℂC2 with ℂC2x66. If you don't yet have ℂC2x66, instead wait until you get it, which should be easy, and then exit ℂC2.</p>
    <p>Set your eternity autobuyer back to <span id="e1211"></span>. Colors of chroma now unlock automatically due to "More colorful than a potato", so you don't need to manually unlock them. Complexity for <span id="e1212"></span> ℂP. This complexity should take <span id="e1213"></span>.</p>
    <p>You now have <span id="e1214"></span> complexities and <span id="e1215"></span> complexity points. Enter ℂC5 before you eternity; if you eternity before entering ℂC5, you will likely buy EG8 automatically first. Unlocking red is easy, even in ℂC5. Get ℂC5x8, and then exit ℂC5 and complexity. This complexity will give <span id="e1216"></span> ℂP. This complexity should take <span id="e1217"></span>.</p>
    <p>You now have <span id="e1218"></span> complexities and <span id="e1219"></span> complexity points. Enter ℂC6. Set the eternity autobuyer to <span id="e1220"></span>. In this complexity, you will try to get "On the other side" and thus complete all complexity achievements. Unlocking chroma should be easy. As before, when you unlock chroma, turn the eternity autobuyer off, get <span id="e1221"></span> grey, then turn the eternity autobuyer back on. Chroma production may sometimes apparently stop for a few seconds. This is because of the permanence autobuyer causing you to lose eternities. Since "After a hurricane" makes chroma faster with more eternities and chroma buildup speed is retroactive, losing eternities will temporarily decrease chroma. This has been going on in the past and happens outside of ℂC6 also; it is just easier to notice now.</p>
    <p>When you unlock purple, turn the eternity autobuyer off and get <span id="e1222"></span> chroma, giving you <span id="e1223"></span> grey and <span id="e1224"></span> purple in the same eternity due to "Shadeless". Then turn the eternity autobuyer back on. After roughly <span id="e1225"></span> in this complexity, you should get "On the other side" and thus complete all complexity achievements.</p>
    <p>In case you get "On the other side" earlier than suggested here, it makes "Forgot something" and "3 * 7 * 11" very easy, since both "Forgot something" and "3 * 7 * 11" can then be gotten with the theorems you have from the previous complexity. Also, only buying theorems in your current complexity stops you from getting "Thousand-theorem twilight", so "Thousand-theorem twilight" is also easier.</p>
    <p>This section of the game (from complexity to completing all complexity achievements) should take roughly <span id="e1226"></span>.</p>
    <p>Here's a shorter-form description of when to get each complexity achievement, if you're using this guide and playing relatively actively. Note that a given complexity challenges doesn't generally help in getting more tiers of itself (exceptions being ℂC1 and ℂC3). Also, exact numbers of each complexity challenge usually don't matter; it's fine if you have one fewer (with the main exception being ℂC1, which is very important).</p>
    <table style="margin-left: auto; margin-right: auto;" style="width: 90%">
      <colgroup>
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 10%;">
         <col span="1" style="width: 20%;">
         <col span="1" style="width: 30%;">
         <col span="1" style="width: 30%;">
      </colgroup>
      <tr>
        <td style="text-align: center;">Order (<span id="e1227"></span> to <span id="e1228"></span>)</td>
        <td style="text-align: center;">Complexities</td>
        <td style="text-align: center;">ℂC completions (ℂC1/ℂC2/ℂC3/ℂC4/ℂC5/ℂC6)</td>
        <td style="text-align: center;">Complexity Achievement</td>
        <td style="text-align: center;">Notes</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1229"></span></td>
        <td style="text-align: center;"><span id="e1230"></span></td>
        <td style="text-align: center;"><span id="e1231"></span>/<span id="e1232"></span>/<span id="e1233"></span>/<span id="e1234"></span>/<span id="e1235"></span>/<span id="e1236"></span></td>
        <td style="text-align: center;">One per generator</td>
        <td style="text-align: center;">Straightforward, fairly soon after IC1</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1237"></span></td>
        <td style="text-align: center;"><span id="e1238"></span></td>
        <td style="text-align: center;"><span id="e1239"></span>/<span id="e1240"></span>/<span id="e1241"></span>/<span id="e1242"></span>/<span id="e1243"></span>/<span id="e1244"></span></td>
        <td style="text-align: center;">Forever isn't too long</td>
        <td style="text-align: center;">You can get this with <span id="e1245"></span> complexities by waiting or already having ℂC1x2</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1246"></span></td>
        <td style="text-align: center;"><span id="e1247"></span></td>
        <td style="text-align: center;"><span id="e1248"></span>/<span id="e1249"></span>/<span id="e1250"></span>/<span id="e1251"></span>/<span id="e1252"></span>/<span id="e1253"></span></td>
        <td style="text-align: center;">Actually a boost</td>
        <td style="text-align: center;">You don't need to do anything special to get this</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1254"></span></td>
        <td style="text-align: center;"><span id="e1255"></span></td>
        <td style="text-align: center;"><span id="e1256"></span>/<span id="e1257"></span>/<span id="e1258"></span>/<span id="e1259"></span>/<span id="e1260"></span>/<span id="e1261"></span></td>
        <td style="text-align: center;">Time after time</td>
        <td style="text-align: center;">Do quick eternities; this will take roughly <span id="e1262"></span></td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1263"></span></td>
        <td style="text-align: center;"><span id="e1264"></span></td>
        <td style="text-align: center;"><span id="e1265"></span>/<span id="e1266"></span>/<span id="e1267"></span>/<span id="e1268"></span>/<span id="e1269"></span>/<span id="e1270"></span></td>
        <td style="text-align: center;">Broke every stone</td>
        <td style="text-align: center;">Remember to turn EC autocompletion off so you can get this</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1271"></span></td>
        <td style="text-align: center;"><span id="e1272"></span></td>
        <td style="text-align: center;"><span id="e1273"></span>/<span id="e1274"></span>/<span id="e1275"></span>/<span id="e1276"></span>/<span id="e1277"></span>/<span id="e1278"></span></td>
        <td style="text-align: center;">No rest</td>
        <td style="text-align: center;">If you aren't close to this with <span id="e1279"></span> in EC2, come back later with more EP</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1280"></span></td>
        <td style="text-align: center;"><span id="e1281"></span></td>
        <td style="text-align: center;"><span id="e1282"></span>/<span id="e1283"></span>/<span id="e1284"></span>/<span id="e1285"></span>/<span id="e1286"></span>/<span id="e1287"></span></td>
        <td style="text-align: center;">Shadeless</td>
        <td style="text-align: center;">Note that you should now have ℂG2 also. This complexity achievement can be done earlier, but unless you're fairly idle it's not recommended.</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1288"></span></td>
        <td style="text-align: center;"><span id="e1289"></span></td>
        <td style="text-align: center;"><span id="e1290"></span>/<span id="e1291"></span>/<span id="e1292"></span>/<span id="e1293"></span>/<span id="e1294"></span>/<span id="e1295"></span></td>
        <td style="text-align: center;">After a hurricane</td>
        <td style="text-align: center;">Straightforward</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1296"></span></td>
        <td style="text-align: center;"><span id="e1297"></span></td>
        <td style="text-align: center;"><span id="e1298"></span>/<span id="e1299"></span>/<span id="e1300"></span>/<span id="e1301"></span>/<span id="e1302"></span>/<span id="e1303"></span></td>
        <td style="text-align: center;">3 * 7 * 11</td>
        <td style="text-align: center;">Straightforward, but requires pushing a little</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1304"></span></td>
        <td style="text-align: center;"><span id="e1305"></span></td>
        <td style="text-align: center;"><span id="e1306"></span>/<span id="e1307"></span>/<span id="e1308"></span>/<span id="e1309"></span>/<span id="e1310"></span>/<span id="e1311"></span></td>
        <td style="text-align: center;">Calm EC</td>
        <td style="text-align: center;">See guide above for which EC tiers to do and when to do each EC tier</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1312"></span></td>
        <td style="text-align: center;"><span id="e1313"></span></td>
        <td style="text-align: center;"><span id="e1314"></span>/<span id="e1315"></span>/<span id="e1316"></span>/<span id="e1317"></span>/<span id="e1318"></span>/<span id="e1319"></span></td>
        <td style="text-align: center;">Power beats knowledge</td>
        <td style="text-align: center;">Build up boost power in a single eternity that's <span id="e1320"></span> long</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1321"></span></td>
        <td style="text-align: center;"><span id="e1322"></span></td>
        <td style="text-align: center;"><span id="e1323"></span>/<span id="e1324"></span>/<span id="e1325"></span>/<span id="e1326"></span>/<span id="e1327"></span>/<span id="e1328"></span></td>
        <td style="text-align: center;">Thousand-theorem twilight</td>
        <td style="text-align: center;">Turn theorem autobuyers off. Use studies 1, 2, 5, 6, 9, 11 for most of complexity (including the end); see above for advice for the start</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1329"></span></td>
        <td style="text-align: center;"><span id="e1330"></span></td>
        <td style="text-align: center;"><span id="e1331"></span>/<span id="e1332"></span>/<span id="e1333"></span>/<span id="e1334"></span>/<span id="e1335"></span>/<span id="e1336"></span></td>
        <td style="text-align: center;">Nonzero-color theorem</td>
        <td style="text-align: center;">Straightforward</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1337"></span></td>
        <td style="text-align: center;"><span id="e1338"></span></td>
        <td style="text-align: center;"><span id="e1339"></span>/<span id="e1340"></span>/<span id="e1341"></span>/<span id="e1342"></span>/<span id="e1343"></span>/<span id="e1344"></span></td>
        <td style="text-align: center;">More colorful than a potato</td>
        <td style="text-align: center;">Straightforward</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1345"></span></td>
        <td style="text-align: center;"><span id="e1346"></span></td>
        <td style="text-align: center;"><span id="e1347"></span>/<span id="e1348"></span>/<span id="e1349"></span>/<span id="e1350"></span>/<span id="e1351"></span>/<span id="e1352"></span></td>
        <td style="text-align: center;">Forgot something</td>
        <td style="text-align: center;">Third-row studies are most expensive so skip one of those</td>
      </tr>
      <tr>
        <td style="text-align: center;"><span id="e1353"></span></td>
        <td style="text-align: center;"><span id="e1354"></span></td>
        <td style="text-align: center;"><span id="e1355"></span>/<span id="e1356"></span>/<span id="e1357"></span>/<span id="e1358"></span>/<span id="e1359"></span>/<span id="e1360"></span></td>
        <td style="text-align: center;">On the other side</td>
        <td style="text-align: center;">You can get this earlier if you're patient, and it helps with "Forgot something", "3 * 7 * 11", and "Thousand-theorem twilight" if you do, but overall unless you're idle I don't think it's worth it</td>
      </tr>
    </table>
  </div>
  <div id="b29">
    <h3>Completing all complexity achievements to unlocking powers</h3>
    <p>After getting "On the other side", exit ℂC6 with roughly ℂC6x22 (but the exact number of completions is not important). Change "Push" to 1,2,3,4,5,6,7,8,9,10,11,12&amp;s9,10,9,3. This allows buying Study 16 when it is very cheap, which will increase total fourth-row study purchases and thus increase the chroma cap slightly.</p>
    <p>Complexity for <span id="e1361"></span> ℂP again, and then enter ℂC2. Do ℂC2x76, ℂC3x38, and ℂC4x17, each in its own complexity and each roughly between <span id="e1362"></span> and <span id="e1363"></span>. You aren't doing ℂC5 because it's weak, and you aren't doing ℂC6 because you just did it.</p>
    <p>Note that at this point, due to Study 16 and its effect being raised to a power, chroma will basically always cap almost instantly.</p>
    <p>From this point on, new complexity generators are of course the most important thing to buy with ℂP, and otherwise it's best to buy the cheapest complexity generator (or the highest one you've bought, if you can buy it and it costs the same amount of ℂP as others).</p>
    <p>Do a complexity for more ℂP. Set the eternity autobuyer to <span id="e1364"></span>. Once you can get <span id="e1365"></span> ℂP on complexity, which should happen roughly <span id="e1366"></span> after complexity, do a long eternity to build up boost power. This increases your highest boost power, which slightly increases complexity generator multipliers (the ℂG1 multiplier might increase roughly <span id="e1367"></span>x). <span id="e1368"></span> is a good amount of boost power to get, and will take roughly <span id="e1369"></span> to reach.</p>
    <p>After getting boost power, turn the eternity autobuyer back on. Unlike in previous complexities, ℂP per second will keep going up. Complexity for <span id="e1370"></span> ℂP (which you can use for ℂG3), which should take roughly <span id="e1371"></span> in complexity (counting the time spent building up boost power).</p>
    <p>Do another complexity for ℂP, getting <span id="e1372"></span> ℂP in <span id="e1373"></span>.</p>
    <p>Do ℂC2x82, ℂC4x19, ℂC5x11, and ℂC6x33, each in its own complexity, of course, and each roughly between <span id="e1374"></span> and <span id="e1375"></span> long, except for ℂC6x33 which will take <span id="e1376"></span>. You can't get enough new ℂC3 completions for ℂC3 to be worthwhile.</p>
    <p>Some general complexity challenge advice follows. ℂC1 and ℂC4 are generally the best ℂCs (ℂC6 becomes good later, once it gives you <span id="e1377"></span> total theorems, but it isn't good yet). In ℂC4, your progress will always stall quickly, so if you can get a completion of ℂC4 in <span id="e1378"></span>, do it, and if not, it's probably practically impossible without more progress. For the other ℂCs, getting <span id="e1379"></span> to <span id="e1380"></span> completions and taking <span id="e1381"></span> to <span id="e1382"></span> when you try each is good. This roughly means that you should do most ℂCs once or twice per squaring of stars (or, roughly equivalently, of ℂP). Once ℂC6 becomes good, even <span id="e1383"></span> completion of it is worthwhile, though.</p>
    <p>Now, turn the complexity autobuyer on (setting it in such a way that it will always complexity) and set the eternity autobuyer to <span id="e1384"></span>. This will let you do complexities that are <span id="e1385"></span> long, which will improve complexity generator multipliers. You should reach <span id="e1386"></span> complexities at this point. At <span id="e1387"></span> complexities you should be able to shorten eternities to <span id="e1388"></span> and still complexity in <span id="e1389"></span> eternities, decreasing the length of each complexity to <span id="e1390"></span>. Note that with more ℂP you could do complexities that were far quicker, but getting more ℂP and then more complexities would be slower overall.</p>
    <p>After getting <span id="e1391"></span> complexities, go back to doing complexities for ℂP, with eternities <span id="e1392"></span> long. Each complexity should be for <span id="e1393"></span>x to <span id="e1394"></span>x total ℂP. Each new complexity generator will increase ℂP gain a lot. Complexities will increase in length from <span id="e1395"></span> to <span id="e1396"></span>. At <span id="e1397"></span> ℂP, you should again do a longer eternity to get boost power, getting <span id="e1398"></span> boost power in <span id="e1399"></span> to <span id="e1400"></span> at the end of a complexity. Unlock powers as soon as you have <span id="e1401"></span> ℂP.</p>
    <p>This section of the game (from completing all complexity achievements to unlocking powers) should take roughly <span id="e1402"></span>.</p>
  </div>
  <div id="b30">
    <h3>Unlocking powers to unlocking galaxies</h3>
    <p>Powers have randomness. Thus, this section and the next section of the guide cannot reasonably give exact strategy. It will instead bring up all the considerations for you to take into account, and say what you want to do no matter what.</p>
    <p>Some general explanation of things you'll probably want to know about powers follows. You can equip up to <span id="e1403"></span> powers at once, and if you want to change your choices for some reason you can unequip your equipped powers (and can later re-equip them if you want). To unequip powers, you need to do a complexity reset or to complexity. You can have multiple powers of the same type equipped, and if you do, their multipliers combine as 1 + (a - 1) + (b - 1) where a and b are their individual multipliers (if there are <span id="e1404"></span>), or 1 + (a - 1) + (b - 1) + (c - 1) where a, b, and c are their individual multipliers (if there are <span id="e1405"></span>).</p>
    <p>The multiplier of a power is generally its strength times its rarity, but there is an additional multiplier for each type of power other than normal which only depends on the power's type (and other properties of the state of your game, but not directly other properties of the power itself). Powers of the same type can be compared by their multiplier (or equivalently their strength times their rarity); a higher multiplier is always better. Stored powers (powers you have but which are not equipped) are sorted by type, and vertically within each type with the best on top. There's no reason to have more than <span id="e1406"></span> powers of the same type, so if you do the worst one will be deleted (for the same amount of power shards as if you deleted it).</p>
    <p>Turn the eternity autobuyer off. Its only use at this point is in ℂC3 for getting eternities (since in ℂC3 you don't produce eternities automatically).</p>
    <p>You start with <span id="e1407"></span> of each of the <span id="e1408"></span> types of power. The best powers to use initially are NIC (normal, infinity, complexity), since an eternity power takes a long time to build up and with NIC you can make progress quickly. Complexities only <span id="e1409"></span> long should let you get to <span id="e1410"></span> ℂP. Do ℂCs again after ℂG7 (just after unlocking powers) or after ℂG8, if you haven't done them recently.</p>
    <p>Some more general complexity challenge advice follows. Since you don't have to eternity, the amount of time to spend on a ℂC is now only <span id="e1411"></span> instead of <span id="e1412"></span> to <span id="e1413"></span>. You can try to do a ℂC for longer than <span id="e1414"></span> at the start of a complexity and, when you're done with the ℂC, exit it and start a normal complexity. This means that ℂGs can still build up while you're in the ℂC. However, the risk of forgetting to leave the ℂC, especially for some ℂCs that aren't that hard, makes this technique usually not worth it in my opinion. (There will, after roughly <span id="e1415"></span>, be a warning if you spend a long time in a complexity challenge.)</p>
    <p>It is very important, for the sake of red (which is stronger with more eternities and which is very important), to get eternities in ℂC3. So, when in ℂC3, either manually eternity several times roughly every <span id="e1416"></span>, or eternity every <span id="e1417"></span> with the eternity autobuyer. Note that eternities depend on the effect of purple, which increases a lot over a complexity, so just getting eternities at the start of ℂC3 will not suffice.</p>
    <p>Going back to the topic of powers, all the power upgrades are very important. They are much more important to buy than complexity generators, with the exception of the first purchase of ℂG8. However, they only apply to new powers you get, so they aren't generally useful immediately. Generally, you should turn power gain off until you get the strength upgrade for <span id="e1418"></span> ℂP (and of course turn it back on after getting that upgrade), unless your first randomly generated power (which you can see as your initial "next power") has rarity under <span id="e1419"></span> (making it likely not worth using anyway). In general, up to <span id="e1420"></span> ℂP, if you're about to get a power upgrade right after you get a power, turn power gain off until you get the upgrade.</p>
    <p>On the topic of ℂP gain, getting between <span id="e1421"></span>x and <span id="e1422"></span>x total ℂP every complexity is good. If you recently got something helpful for ℂP, like a very good power or (later) a ℂC4 completion, you might want to complexity for a higher multiplier than <span id="e1423"></span>x right after getting it (and, in the case of a power, equipping it), if you can reach a higher multiplier in <span id="e1424"></span>. If you suddenly get a good new power (significantly better than your current powers), you'll probably want to complexity and equip it, even if you don't gain much ℂP from doing so.</p>
    <p>If you are using an eternity power, the above paragraph's suggestion of <span id="e1425"></span>x to <span id="e1426"></span>x ℂP is too low. Indeed, at least for this section of the guide, playstyle when using an eternity power is very different than it is otherwise. If you use an eternity power, it is best to do much longer complexities (hours initially, going down to roughly <span id="e1427"></span> by the end of this section), because an eternity power takes time to build up.</p>
    <p>Obviously this extra complexity length means you need a lot more ℂP each complexity for this to be worthwhile. Indeed, if you are active and do not have an eternity power that is extremely good (for example, <span id="e1428"></span> higher multiplier than your other powers), using an eternity power is only near as good as not at the end of this section (after <span id="e1429"></span> ℂP). Before that, an eternity power is bad. However, if you are idle and only want to look at the game every hour, or if you are doing an overnight complexity, or if you have an extremely good eternity power, or (in some cases) if you're at a wall and want to do something to get past it, an eternity power is likely the right choice.</p>
    <p>Going back to early progression in this section of the game, in getting to <span id="e1430"></span> ℂP, your longest complexity should be <span id="e1431"></span> at most. This of course assumes you are not using an eternity power. At this point, the best powers for ℂP are normal powers, with infinity powers somewhat worse, eternity powers as discussed above, and complexity powers a lot worse than infinity powers but still better than eternity powers for short runs. Basically, as soon as you get <span id="e1432"></span> powers that are either normal or infinity that all have multiplier at least <span id="e1433"></span>, you should use those for ℂP (unless you are using an eternity power, or your powers of other types are very good).</p>
    <p>At this point you should probably create a power preset (called "Push" in this guide, but I guess you can call it something else if you want) for complexities in which you get ℂP. Note that "probably" here depends on your style of play, and mostly not on the game's random number generator; this power preset will change, or additional ones will be added, several times before finality. However, despite that, I found having a power preset to be convenient. As with a study preset and the Studies tab, you can create a power preset at the bottom of the Powers tab. Either create the preset when you have your ℂP gain powers (primarily normal and infinity) equipped, or create a new preset and make it the <span id="e1434"></span> powers abbreviations you want equipped, where N, I, E, and C are normal, infinity, eternity, and complexity respectively. Power presets are stored in the save (which doesn't handle unicode well) and most keyboards don't have ℂ, which is why C is used instead. You might try to make a power preset NNN when you don't have <span id="e1435"></span> normal powers; in this case the game will equip as many normal powers as you do have when you load the preset (it won't throw an error, or suddenly create normal powers out of nowhere and equip them).</p>
    <p>Now that you're generally not using your complexity power, you should still use it (or them, if you've gotten more than <span id="e1436"></span>) sometimes to get more complexity stars. Now, you're probably wondering what you're going to use those complexity stars for. After all, you'll lose them when you complexity and go back to using the Push preset. But to answer that, we need to talk about "On the other side". And if you thought the other parts of complexity were complicated, just you wait.</p>
    <p>The way "On the other side" works is you keep bought theorems, but you also keep each type of extra (non-bought) theorem. For example, if you somehow get "On the other side" before "Calm EC", you'll start every complexity with <span id="e1437"></span> theorems from EC completions anyway. Theorems from ℂC6 are a type of extra theorem, and how many you have depends on two things, which are ℂC6 completions and complexity stars (because complexity stars make ℂC6 stronger). So getting more complexity stars increases extra theorems from ℂC6. Since you keep extra theorems, you keep these theorems even after switching to another preset. Now, these theorems might not let you buy another study, but "Nonzero-color theorem" increases the chroma cap linearly based on theorems (it multiplies the chroma cap by (<span id="e1438"></span> + theorems / <span id="e1439"></span>)). So more theorems are very helpful. Note that increasing the chroma cap is mostly helpful because of the effects of purple and red.</p>
    <p>Whenever you gain more ℂP (and thus more complexity generators) or more ℂC6 completions, you can quickly get a large number of extra theorems by using complexity powers. So for best results, you would briefly switch to complexity powers every time you gained ℂP or ℂC6 completions. Doing this is a large speedup but not mandatory.</p>
    <p>If you've used complexity powers recently, you'll probably need to use them again to get anything from a ℂC6 completion, since the extra ℂC6 completions aren't so strong that ℂC6 will give more extra theorems than it gave with complexity powers.</p>
    <p>Of course, if you just complexitied, you should buy complexity generators before or while using complexity powers, not after. If you first switch to complexity powers, then switch back, and then buy complexity generators, you won't get the extra theorems that would have come from having higher complexity generator multipliers and thus more complexity stars while your complexity powers were equipped. This might seem somewhat intuitive, but you (or at least I) can easily mistakingly buy complexity generators afterwards.</p>
    <p>There's not much use to using your complexity powers for that long. The complexity star gain from waiting doesn't give many more theorems. <span id="e1440"></span> seconds in a complexity with complexity powers should be enough.</p>
    <p>If you don't yet have <span id="e1441"></span> complexity powers, also use your other powers with highest product of strength and rarity when using complexity powers. Since complexity powers get an extra multiplier based on strength and rarity of equipped powers, this will maximize that extra multiplier.</p>
    <p>Once you have <span id="e1442"></span> complexity powers, you should create a preset called "Complexity" which is CCC, to make it easier to equip your complexity powers.</p>
    <p>Complexities in this phase will generally be about <span id="e1443"></span> long, shorter when you get a good new power and longer if you are using an eternity power (in this pre-galaxy phase, <span id="e1444"></span> is almost a minimum length if you're using an eternity power).</p>
    <p>If you're playing actively, you probably won't be using eternity powers much, so feel free to delete any that aren't especially good (higher total multiplier than your normal and infinity powers). In general, if you're sure you won't use a power, you can delete it. However, since powers are automatically deleted when you have enough better powers, this doesn't give you too many extra power shards compared to using power shards from automatically deleted powers, except very early on (your first <span id="e1445"></span> powers or so).</p>
    <p>The most important power shard upgrades to buy are those for powers you use the most of. However, you should generally keep all power shard upgrade costs for power types you use at all within a factor of <span id="e1446"></span> of each other (in this phase, those power types are likely at least everything but eternity, and also eternity if you're idle).</p>
    <p>Crafting powers is sometimes useful, especially if you feel like fewer than expected of the random powers you're getting are good. Crafting lets you create powers of a given type and rarity, for a cost in power shards. In this phase of the game, crafting is on average slightly less efficient than waiting for random powers, but of course this depends on which random powers you're going to get. Generally, crafting normal powers is best in this part of the game, but right before unlocking galaxies crafting an infinity power becomes perhaps slightly better (especially if you're not using any infinity powers), and if you're very idle crafting an eternity power might be worth it.</p>
    <p>As suggested by the suggestions above for what types of power to craft, when you're trying to get more ℂP, NNN (all normal) is generally best (unless you're using an E (eternity power) as described above), with NNI becoming good near galaxy unlock or if you get a great infinity power, and NII or III being good if your infinity powers are extremely good compared to your normal powers. IEC and NEC are good powers to use if you're using an eternity power, since the C gives you more complexity stars and makes the E build up faster.</p>
    <p>In ℂC4 specifically, NNC or (if you have no good C) NNN is good. Note that ℂC4 completions are very important. It may be worth creating a preset.</p>
    <p>The Oracle is a very useful feature, even though it only gives you information. It lets you know roughly what your game state will be in the future. It has two main usages. One usage is comparing sets of powers without actually doing long complexities with then (this is especially important for eternity powers since they take time to become good and you don't want to waste that time if in fact they're not good). The other usage is seeing what powers you're going to get and when, so you can plan accordingly and can avoid getting a great new power just after starting a long run, or randomly getting a power similar to one that you just spent a lot of power shards crafting.</p>
    <p>You should have the alert option on so that you can press O on another tab (like the powers tab) and get a brief description of the consequences of your powers. Note that with enough ticks, the Oracle might take a few seconds to work (it will show a progress bar on the top of the screen during this time), but the more ticks you're using the more accurate the predictions will be (<span id="e1447"></span> ticks is usually enough, though).</p>
    <p>After <span id="e1448"></span> ℂP, Study 14 is by far more useful than the other fourth-row studies; the main benefit from other fourth-row studies is their small increase to the chroma cap. Change your Push study preset to 1,2,3,4,5,6,7,8,9,10,11,12&s3,10,3,3 to further prioritize Study 14.</p>
    <p>After <span id="e1449"></span> ℂP, the game largely consists of waiting for good enough powers (either via random generation or via crafting) to unlock galaxies. You'll probably need powers with rarities <span id="e1450"></span> to <span id="e1451"></span> to unlock galaxies. Even a <span id="e1452"></span> increase in rarity in <span id="e1453"></span> power is noticeable.</p>
    <p>How long unlocking powers to unlocking galaxies takes is variable, but <span id="e1454"></span> is a typical amount of time.</p>
  </div>
  <div id="b31">
    <h3>Unlocking galaxies to finality</h3>
    <p>Unlocking galaxies give you autobuyers for complexity generators and power upgrades, so you don't need to buy those manually anymore. Due to needing to use CCC for theorems, however, auto-complexity is still not good.</p>
    <p>More importantly, galaxies increase the chroma cap over time by raising it to a power, which starts at <span id="e1455"></span> and increases over each complexity to some cap based on how many galaxies you have. There are three main impacts this has on play. The first effect is to make long complexities better. This may make IEC better than whatever powers you're using. On the other hand, it might not. Use the Oracle to find out (using an amount of time roughly equal to the time galaxies take to cap). The second effect is to encourage getting more galaxies, which is almost but not exactly the same as making more general progress. CCC is good for getting galaxies because it gives you more total complexity stars, and IEC gains the additional advantage that your additional total eternity stars may give you another galaxy. Using more than <span id="e1456"></span> E is not worth it, however, because you then can't get as much EP which generally more than cancels out the additional power to EGs.</p>
    <p>The third effect of galaxies on gameplay is the decision of how many galaxies to dilate. The galaxy power on chroma increases quicker the more dilated galaxies you have; the speed multiplier is (<span id="e1457"></span> + dilated galaxies)^<span id="e1458"></span>. However, dilated galaxies don't count towards increasing the cap, so if you dilate all your galaxies, then galaxies don't increase the chroma cap at all. (Thus dilating all your galaxies is a bad idea.) Generally dilating all but <span id="e1459"></span> (or, later, when you're near finality, all but <span id="e1460"></span>) of your galaxies is good if you're active. If you're idle or doing an overnight run, dilate fewer galaxies. (But once you have <span id="e1461"></span> galaxies or so, you should basically always dilate at least <span id="e1462"></span> galaxy no matter what.)</p>
    <p>It's worth noting that after the first few galaxies, each galaxy increases the time for the galaxy effect power to reach its cap by more than the last (which is why dilating galaxies becomes basically necessary).</p>
    <p>Galaxies also increase the strength of new powers somewhat, but this doesn't affect gameplay much qualitatively.</p>
    <p>As for how long complexities should be, once you unlock galaxies you generally want to get the galaxy effect to its cap in each complexity. After roughly <span id="e1463"></span> ℂP, if you're using an eternity power (as you probably are), you probably want the eternity power extra multiplier to cap at <span id="e1464"></span>x also. (Ideally the galaxy effect and your eternity power cap at about the same time, but this is not very important.)</p>
    <p>This does not apply in challenges, which you should generally only be in for <span id="e1465"></span> to <span id="e1466"></span>, even if galaxies don't cap that quickly (as they almost surely won't). Since complexities with challenges are shorter, it might be better to use NNI, NII, or III for challenges. However, further along (perhaps at <span id="e1467"></span> ℂP), as eternity powers build up faster due to more complexity stars, IEC may be better in complexity challenges.</p>
    <p>Note that after <span id="e1468"></span> ℂP, the eternity power extra multiplier will cap before the galaxy effect caps. If the galaxy effect caps first, you are probably dilating too many galaxies and should probably try dilating fewer.</p>
    <p>Powers to use for getting ℂP are IEC initially, switching to IIE (or IEE if you have no good I or only one good I) at roughly <span id="e1469"></span> ℂP. For ℂC4, it's best to use NCC after roughly <span id="e1470"></span> ℂP (when you unlock galaxies) and to use CCC after roughly <span id="e1471"></span> ℂP.</p>
    <p>How long unlocking galaxies to finality takes is variable, but <span id="e1472"></span> is a typical amount of time (yes, roughly the same as for unlocking powers to unlocking galaxies).</p>
  </div>
  <div id="b32">
    <h3>After finality</h3>
    <p>So, you've finalitied. As with eternity and complexity, this resets basically everything. You keep your slow autobuyers, and that's basically it. However, you do have <span id="e1473"></span> finality points (FP) and <span id="e1474"></span> finality shards.</p>
    <p>You may have noticed that you hit a star hardcap right before you reached finality. That star hardcap is there to stay. There's no way to get rid of it or push it back, and the rest of the game is about reaching it quicker and quicker.</p>
    <p>With your <span id="e1475"></span> FP, you can, and should, buy a Finality Generator 1. Finality generators (FGs) are like previous generators except that they cost finality points. Finality stars have the effect of multiplying all previous generators (normal, infinity, eternity, and complexity) by <span id="e1476"></span>^(log<span id="e1477"></span>(number of finality stars)^<span id="e1478"></span>). This is very strong early in each prestige layer, but is hard to notice in later parts of each prestige layer because all the generator multipliers are so big that this extra multiplier is comparatively small. In practice, this means that the FG multiplier speeds up early eternity in an easy-to-notice way (roughly up to unlocking the Eternity Producer) and also speeds up early complexity (roughly up to unlocking powers), but between the Eternity Producer and complexity and between power unlock and finality, finality stars won't do much.</p>
    <p>Note that the finality star per-purchase multiplier depends on finalities; it's <span id="e1479"></span>^(min(<span id="e1480"></span>, max(<span id="e1481"></span>, finalities^<span id="e1482"></span>)) / <span id="e1483"></span>). This starts at the usual <span id="e1484"></span>^(<span id="e1485"></span> / <span id="e1486"></span>) but can increase up to <span id="e1487"></span> eventually. This is in addition to the multiplier to finality generators of min(<span id="e1488"></span>, finalities / <span id="e1489"></span>).</p>
    <p>Fortunately, there are other benefits given by finality. The most notable are finality shard upgrades. You get <span id="e1490"></span> times your finalities shards each finality (so <span id="e1491"></span>, <span id="e1492"></span>, etc.), with the only (unimportant) exception being that you instead get twice that many shards on finalities divisible by <span id="e1493"></span> (this is unimportant because by <span id="e1494"></span> finalities, finalities will be very fast; it's only included to make certain numbers line up). There are <span id="e1495"></span> finality shard upgrades, described below. The first <span id="e1496"></span> can be bought up to <span id="e1497"></span> times; the other <span id="e1498"></span> can only be bought up to <span id="e1499"></span> times.</p>
    <p>Power to non-finality generator multipliers: This raises all multipliers of non-finality generators to the power of <span id="e1500"></span> + times bought / <span id="e1501"></span>. This is very noticeable in eternity after roughly <span id="e1502"></span> EP. In powers it becomes slightly harder to notice, but is still important. For comparison, the effect this has on normal generators (which is most of its effect) is equivalent to a normal power with strength and rarity <span id="e1503"></span> (before power shard upgrades).</p>
    <p>Finality point gain on finality: This has a messy formula. At first it's just <span id="e1504"></span> more per purchase, but it eventually becomes a lot stronger and reaches <span id="e1505"></span> when it caps. This is the only way to get additional FP per finality. It's mostly worthwhile when it'll give you a new finality generator you have none of yet.</p>
    <p>Multiplier to eternity and permanence gain: The formula for this is (<span id="e1506"></span> + times bought)^<span id="e1507"></span>. This is mostly noticeable between eternity and chroma. It makes eternity milestones a lot easier to deal with, and since it multiplies eternities and permanence it basically acts as a (<span id="e1508"></span> + times bought)^<span id="e1509"></span>x multiplier to permanence. Still, before you get far into chroma this becomes harder to notice.</p>
    <p>Multiplier to chroma buildup speed: The formula for this is also (<span id="e1510"></span> + times bought)^<span id="e1511"></span>. This is useful when chroma is slow, which is during your first few complexities of your first few finalities but never again. This is probably the weakest of the upgrades, overall.</p>
    <p>Multiplier to chroma cap: The formula for this is (<span id="e1512"></span> + times bought / <span id="e1513"></span>)x. When you first unlock chroma, this is probably less helpful than "Multiplier to chroma buildup speed", but unlike "Multiplier to chroma buildup speed" it keeps doing something throughout. Its effect on chroma cap is significantly less than that of galaxies, though (note that <span id="e1514"></span> galaxy raises the chroma cap to the power of <span id="e1515"></span>, which is a lot stronger because it's a power rather than a multiplier).</p>
    <p>Multiplier to power gain speed: The formula for this is, yet again, (<span id="e1516"></span> + times bought)^<span id="e1517"></span>. This is probably the most important finality shard upgrade. It's true that it only affects things once you have powers, but at that point not much else is doing anything (mostly "Power to non-finality generator multipliers" and "Multiplier to chroma cap") so powers can be very slow without this.</p>
    <p>Increase to strength of new powers: The formula for this is +(times bought / <span id="e1518"></span>). This upgrade works similarly in practice to "Multiplier to power gain speed", but is weaker early. This is true both early in each finality, since power strength varies a lot right after you unlock powers anyway and getting more chances is thus more valuable than a small increase, and early overall, since a <span id="e1519"></span>x (from the first purchase of "Multiplier to power gain speed") or <span id="e1520"></span>x (<span id="e1521"></span> / <span id="e1522"></span>, from the second) multiplier to power gain are both really strong and "Increase to strength of new powers" can't compete much.</p>
    <p>Multiplier to galaxy effect buildup speed: The formula for this is, as you might expect by this point, (<span id="e1523"></span> + times bought)^<span id="e1524"></span>. This is less important than the power finality shard upgrades but still important near the end of each finality. Note that if you don't want to wait as long for galaxies, you can just dilate another galaxy even without this upgrade; this isn't as true for powers, which is what makes this upgrade weaker.</p>
    <p>In addition to their effects, finality shard upgrades give you bonuses based on how many you've bought (counting multiple purchases of the same one as multiple). You get <span id="e1525"></span> stars at the start of each prestige, infinity, eternity, complexity, and finality, with that number of starting stars squaring for every <span id="e1526"></span> upgrades. You also get starting IP, EP, and ℂP equal to the number of each you could get with your starting stars (<span id="e1527"></span> if you don't have enough starting stars for that). You also get <span id="e1528"></span>^min(4, upgrades bought / <span id="e1529"></span>) (rounded down) complexities at the start of finality. Lastly, you get <span id="e1530"></span> starting complexity achievement for every <span id="e1531"></span> upgrades (going left-to-right, top-to-bottom) and <span id="e1532"></span> extra galaxy for every <span id="e1533"></span> upgrades.</p>
    <p>The way this all ends up playing out is that early on, you want finality shard upgrade bonuses as strong as possible so you can start with more complexity achievements. This means not buying any upgrade more than <span id="e1534"></span> time more than any other upgrade. The numbers of extra complexity achievements you can thus get are <span id="e1535"></span>, <span id="e1536"></span>, <span id="e1537"></span>, <span id="e1538"></span>, <span id="e1539"></span>, <span id="e1540"></span>. After <span id="e1541"></span> finalities you can get exactly <span id="e1542"></span> of every finality shard upgrade, which gives you all complexity achievements to start with (this is the <span id="e1543"></span> from the previous sentence).</p>
    <p>If you replay the game, you can import "replay mode" in the save import prompt to see all tabs from the start, if you want (and you can import it again to undo this). This is at a random point in this section to make it slightly harder to find. This mode spoils things, of course, if you haven't played through the game, but if you're reading this you're probably not too worried about that.</p>
    <p>Before you have <span id="e1544"></span> finalities, you won't start with Calm EC (and before <span id="e1545"></span> you won't start with Broke Every Stone). This is annoying, but there are two other things that ameliorate it. One is finality milestones. The first finality milestone halves the requirements for complexity challenges, meaning you only need <span id="e1546"></span> complexities to do ℂC6 and get Calm EC (and only <span id="e1547"></span> for Broke Every Stone). The second finality milestone, in addition to permanently automating complexity generators and power upgrades (but not power shards upgrades), removes complexity requirements for complexity challenges entirely.</p>
    <p>However, even with the finality milestone for 2 finalities, it's still wise to first do a normal first complexity, then do a second complexity where you get ℂC2, ℂC3, and ℂC4 completions (likely getting Broke Every Stone, and stopping each when it starts to feel at all hard) and also perhaps some more ℂC1 completions (though you'll also have some of these from your first complexity), and only then go for Calm EC which should then be pretty easy. Note that in general, if a complexity challenge feels hard you should do other ones first.</p>
    <p>With all of this, you'll still be doing eternity challenges roughly <span id="e1548"></span> times (some of which will be cut short by getting Calm EC). Most of these times will just be frantically clicking. If you're more idle, the other thing that ameliorates not having Calm EC is improvements to automatic EC completion. You now automatically complete an EC tier every <span id="e1549"></span> / min(<span id="e1550"></span>, finalities) seconds, and the automatic completions from complexities are <span id="e1551"></span>x faster (every <span id="e1552"></span> / min(<span id="e1553"></span>, complexities) seconds, which helps once you have any complexities). This will also help a lot when you have <span id="e1554"></span> complexities and <span id="e1555"></span> finality. It's not that worth planning out your EC automatic completions, but you'll likely get <span id="e1556"></span> or <span id="e1557"></span> at least before you complete any ECs manually.</p>
    <p>Strategy is pretty straightfoward; it's like before, except you should keep going if things feel fast. For example, your complexities right before powers can be for more than <span id="e1558"></span>x ℂP. As for powers and galaxies, dilating <span id="e1559"></span> more galaxy and using NII or III longer (even after unlocking galaxies) and IEC longer are good strategies; it's worth using the Oracle or intuition to see when to switch powers. Note that eternity power extra multiplier isn't sped up by anything yet, which makes power sets with E comparatively weaker (because you won't be waiting as long).</p>
    <p>The finality you do with <span id="e1560"></span> finality will be split between first few complexities (mostly frantic clicking, with some waiting in first complexity) and powers (mostly waiting). It can take as short a time as roughly <span id="e1561"></span> (<span id="e1562"></span> for first complexity, <span id="e1563"></span> for first complexity to unlocking powers, <span id="e1564"></span> for unlocking powers to finality).</p>
    <p>Finality times can be as short as roughly <span id="e1565"></span> (as previously stated), <span id="e1566"></span>, <span id="e1567"></span>, <span id="e1568"></span>, <span id="e1569"></span>, <span id="e1570"></span>, after which speedups are largely due to finality milestones automating things that would have taken time to click. Descriptions of the effects of finality milestones will be given below.</p>
    <p>With <span id="e1571"></span> finalities, you get a milestone removing complexity challenge requirements and automating complexity generators and power upgrades (as discussed above). With <span id="e1572"></span> finalities, you get a milestone giving you <span id="e1573"></span> ℂP, which lets you get effects from complexity challenge completions even before doing a complexity. This isn't too significant (it might help you get more ℂC1 completions in your first complexity though).</p>
    <p>With <span id="e1574"></span> finalities, you get a milestone letting you keep ℂC completions. The number you can keep is <span id="e1575"></span>^(min(<span id="e1576"></span>, complexities) / 2), rounded down. Of course you can't keep more than you have, so the min with <span id="e1577"></span> does nothing since you can't get <span id="e1578"></span> completions. Anyway, this will help a lot early on. You don't have to do too much to take advantage of it. Technically after you keep all your ℂC completions you can try to reach the star hardcap in every challenge but ℂC4, but this won't happen for a while and won't be too helpful anyway.</p>
    <p>The milestones for <span id="e1579"></span> through <span id="e1580"></span> finalities are fairly self-explanatory. Once you automatically gain permanence every second you can turn your permanence autobuyer off, which reduces lag a little. Once you unlock study list auto-load you can constantly load Push. Unlocking autobuyers for power shard upgrades is a bit of quality of life (it does mean you might have fewer shards to craft powers with but at this point crafting powers isn't too helpful). Always having EP generation makes getting to powers less painful.</p>
    <p>At this point (in fact, at <span id="e1581"></span> finalities), you'll have capped all but <span id="e1582"></span> finality shard upgrades. You should try to keep those roughly even. You can try to focus on the second one if you're near a new finality generator and could get it with, say, <span id="e1583"></span>x more finality points, and focus on the first otherwise, but it's not that important.</p>
    <p>The milestones for <span id="e1584"></span> through <span id="e1585"></span> finalities and for <span id="e1586"></span> and <span id="e1587"></span> finalities are fairly self-explanatory. The milestone for <span id="e1588"></span> finalities might be a bit confusing but it basically just serves to remove the need for swapping in CCC, so there's no real reason to use CCC (except in ℂC4); you get the theorems you would have gotten from CCC even without using it. The milestone for <span id="e1589"></span> finalities means you only have to swap powers manually if you want different types of powers equipped. For the milestone for <span id="e1590"></span> finalities, IEC are good equipped powers to load.</p>
    <p>Once you get <span id="e1591"></span> finalities, you can set your complexity autobuyer to roughly <span id="e1592"></span> seconds, set your dilated galaxies to <span id="e1593"></span> in "seconds to reach cap" mode (or however many seconds to reach cap your complexity autobuyer is), and turn your finality autobuyer on. Finalities should initially take roughly <span id="e1594"></span> long. Keep buying finality generators and finality shard upgrades.</p>
    <p>The milestone for <span id="e1595"></span> finalities will help a little (it will make your eternity power and galaxies slightly faster due to giving them a few seconds of free time) and the milestone for <span id="e1596"></span> finalities will help a lot. Once you get <span id="e1597"></span> finalities, you can turn your complexity autobuyer off. Finalities should be roughly <span id="e1598"></span> long with it off. Soon starting bonuses of stars/IP/EP/ℂP will become significant and make finalities faster.</p>
    <p>At <span id="e1599"></span> finalities, you'll max out all finality shard upgrades, which will make your starting benefits of stars/IP/EP/ℂP the same as their values at the star hardcap. This lets you finality immediately and is for fairly clear reasons thus the end of the game. This part of the game (finality to end) takes roughly <span id="e1600"></span> (roughly <span id="e1601"></span> of which is spent in second finality and <span id="e1602"></span> of which is spent beyond).</p>
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